Pretty feasible I would think. 

Roughly, handhelds can match home console specs within 8 years. There are times where it was even quicker than this. The Sega Game Gear released 5 years after the Sega Mark III (Master System) and had nearly identical performance. However, the battery consumption was really bad. The TurboExpress came out 3 years after the TurboGrafx-16, but gobbled power like crazy and was expensive.

The PSP seems around the performance of a Dreamcast, and came out 6 years after that console.

A PS4-like handheld might try a 720p display to save money. It would probably also have to be at the very least thicker and at least as wide as the Switch to accommodate the battery and other components. So kind of like the SteamDeck.

You can change Playstation fans to Playstation customers I guess...

Anyway, we need to understand what games people want to play and how exactly the said people want to play. Maybe you misunderstood Switch success as a reflex of how big handheld market really is, but dedicated handheld market is not really that big. The Switch success comes mostly from its hybrid aspect and the consolidation of Nintendo software that used to be apart in a single SKU. 

The realistic ceiling for a handheld-only hardware in the market must be more in line with 3DS numbers i.e. ~75 million. It's a big market still, but we need to understand 3DS inherited DS userbase, they play the same games and most of DS franchises were present in 3DS. There is (big) a fandom, a group of consumers, who until 3DS only ever bought Nintendo as handheld manufacturer 

I don't think an equivalent group exists for Sony, or if they exist should be a very restrict in numbers. Sony customers, at mostly, play Playstation home consoles. All the software they want to play are on PS5 already. It means Playstation users at most aren't really waiting for next Sony handheld, there won't be as much excitement and loyal buyers as for a Nintendo's handheld. Early sales sometimes defines the faith of a hardware and this is very hard do turn around a bad sales trend

If Sony really wants to enter on handheld market again they will need to release something not only very cheap, but with a value proposition that is very hard to ignore. 

For instance, steam Handheld has the fact you can carry your already existing library that you could have built for more than a decade. If Sony smart-delivery your digital library from PS5 to PS5-Portable it maybe can hold similar value, but what about the physicals? We are also talking about console market, the purpose of console market is to sell hardware at loss and then recover with software sales and subscription, if Sony really delivery 100% of digital purchases from PS5 to PS5-Portable how much more software customers will need to buy to offset selling 2 hardwares at loss? 

No, because costs alone for such a device would make it near impossibility. I cannot see device that would have great of an appeal for barebones version of PS5. Who does PS5 Portable appeal to if their device costs $499+ with crappy battery life, if the base PS5 is $199-$299.

I'm not even getting into what logistics of it would need to be with cooling, chipsets.

This.

As I've said, impressive handheld specs don't tend to move hardware units. With home consoles it's pretty similar, but specs are more relevant in home console popularity. 

Almost all of the Game Boy, Game Boy Color, and Game Boy Advance competitors were pretty much a full generation ahead in specs. It didn't stop Nintendo's dominance.

The PSP was far more capable than the DS, and yet it only managed to sell over half of the DS lifetime hardware units.

The Vita got stomped by the 3DS.

Charging too much for a handheld in particular is a recipe for disaster. Why would people pay $450 and up for a dedicated handheld more powerful than a PS4 when by 2023/2024 they'll probably be able to get a PS5 for $300?

Specs don´t define so much, for portable and stationary consoles. Nintendo won on portable because of games. Nintendo never treats your portable space like a second-class citizen, the other companies do this. It´s why Nintendo always stomps all direct competition in portable space. The minor force is Nintendo understands better portable space than their rival. Gameboy fights against Lynx and GameGear two portable with battery problems( Nintendo´s game watch expertise and Gunperi vision helps a lot). GBC fight against Wonderswan one portable focus in Japanese market towards more to niche games, then you have DS fight against PSP and the UMD disc problems. Vita lost against problematic 3ds because Nintendo see the 3d free glass feature is not a premium feature, and then slash the price and launch more portables games and fewer 3d  free glass focus games. 

The were a number of factors that impacted the Vita's success, you have just off the top of my head the more publicised factors like costly proprietary memory the lack of R3/4 triggers these along with Western driven marketing giving the Vita a PS4 lite focus shifted away from what helped make the PSP successful.

The blame for those decisions and their impact can be laid at Sony's door, while those decisions were poor. they would normally have been seen as redeemable setbacks to be turned around, but the market that the Vita entered wasn't the same one that the PSP had found success in. the market changing with the move toward mobile and how we play on the go beside making Sony's mistakes irredeemable and putting an end to the Vita, it pretty much killed any chance of any successor.

Nintendo along with the failure of the Wii U faced a shrinking dedicated handheld market and a future where mobile gaming competition through the use of improved cloud and scaling technology is not just limited to phones with games being available on a range of devices and modes of delivery,could no longer rely on it's two pillar system but could use it to create a hybrid console. If Nintendo was forced to go in that direction why would Sony look to go back to a almost non existent dedicated handheld market where history shows software sales to hardware ratios are half the number of home consoles.

It's fine for Valve the Steam Deck isn't trying to compete as a traditional handheld they don't need to produce games for it or gather 3rd party behind them that's because they  have the steam store and those games and sales are what this is centred on, giving PC gamers another option and another way to access and buy the steam stores tens of thousands of games is its attraction and the real benefit for valve.

Downgrading silicon to hit various formfactors, TDP and power consumption targets has been a thing for decades.

So I wasn't really surprised.
In-fact I argued Nintendo could have gone down the same path by opting for AMD mobile hardware before Tegra got confirmed by Nintendo themselves.

It's easier to scale a game up as newer/faster hardware is released or just simply let it run better automagically through scalable game engine design that uses things like dynamic resolutions/uncapped framerates.

Not really feasible to release a weaker SKU after powerful hardware has already been dropped... Games need to be reworked so performance doesn't bog down.

Microsoft is likely in a better position here as the Xbox Series S is a fairly low baseline as far as hardware is concerned, so theoretically in a few years they could release a mobile device that has the equivalent or better capabilities of the Xbox Series S in a handheld.

Hopefully they do.

Microsoft is entering mobile in a big way with xCloud... And hopefully Sony enters with their own approach... And as we know, Nintendo is dominating this market.

What does that mean for us, the consumer? Potentially more innovation and lower prices. Win, win.

Sony and Microsoft don't really set the resolution, that is up to game developers, the hardware dictates what level of resolution we typically see as it is the hardware holding it back.

I.E. The Xbox Series S due to it's significantly inferior hardware tends to fall around the 1080P-1440P area... However developers can run games at 4k on that system as we saw with Ori and the will of the wisps... And other games significantly come up short of 1080P.
All up the developer and how they intend to prioritize their finite system resources.

The PS5 isn't made for portable technology, even Valve is machine is only a bit better than a PS4 and to achieve that it already costs over € 400,-. To make a device with the strength of a Xbox Series S handheld will not be feasible with a decent battery life before this gen is over.

Valve's machine is closer to the Series S than it is to the PS4.

In about 3 years, you'll have a Series S spec Valve machine at $399. The battery will not be great but the base Switch couldn't play Zelda for more than 3 hours but that didn't stop its appeal. 

If the PS5 is consuming 200W at this point you would need to be at least 10x more efficiënt to consider a portable console. With 5nm they could scale power consumption with the same power 30%. That would mean (considering not just apu but also other components could require less) around 140W for the same performance. When apple will move to 3nm or 4nm for the 2022 iPhone it would free up a lot of current 5nm space that AMD can use. Late 2022 a ps5 slim would be possible on this node.

3nm uses another 30% less power for the same performance. So a ps5 of 100W would be possible on that node. Maybe the total package could reach 70W with some architectural improvements and improvements on chipset, storage ram etc. Still not enough for a portable console. They would need to cut that by 2/3 meaning you gotta make concessions like with the Series S.

So although possible to make a 1080p handheld in 2 to 3 years it would change the strategy completely. That seems unlikely. In 5-6 years from now It should be possible.