It'll definitely cost more to create a Switch-like version of the PS4. I'm not sure if the tech is there yet that could also maintain a reasonable battery life and at a competitive price point. If people are complaining about the Switch's battery life, then I find it hard for people to praise the battery life of a Switch-like PS4 at this point in time.

If they try to make their own hybrid to compete with the Switch, they would have to go all in on it and make that their one system going forward, and even then, they would still be at a big disadvantage. 

The Story: 
Sony has competed with Nintendo on the portable/handheld market for 2 generations, and in both generations, they had the same strategy. 

The Advantage:
Have a more powerful handheld than theirs that delivers a gameplay experience that is close to our consoles. 

The Disadvantage:
However, this has led to the PSP and Vita being more expensive and consume more battery, leading to a shorter battery life. 

The Score:
Nintendo, 2, Sony, 0.

If it didn't work the first two times, I don't see how it's going to work the 3rd time, even if they go all in with that system, because Nintendo is now going all in with theirs. 

If they try to release a "PlayStation Switch" with upgraded and better graphics that bring it on the same level as the PS4, or if that's what ends up being PS5, 3-4 years from now, with the type of graphical upgrade we are now expecting it to be over the PS4 Pro, we're looking at the PS3's launch price all over again. In fact, it could very easily be higher. Are all the people who bought a PS4 for $400 or a Switch for $300 going to buy a PS5/PlayStation Switch for $600 or more? I don't think so.

In my opinion, in order for them to have a realistic and reasonable shot at competing with Nintendo in the portable market, which will now become the hybrid market, they're going to have to bite the bullet on power and graphics. So, that they can have a chance to offer their system at a lower price and/or consume less battery. 

But, they also take a big risk by doing that. Because, if they do, that leaves the dedicated home console market, the market that Sony is the undisputed King and absolutely dominating at the moment, in its entirety, to Microsoft. And all the people who bought a PS4 or PS4 Pro because they were the most powerful consoles on the market at their time, to get the best graphical experience on a console; A good chunk of them are going to jump to Microsoft to get that experience. The Xbox One X has managed to exceed most people's launch expectations, which suggests that some of those people might be doing that already!

So not only does Sony drop out of their own main market and lose a big chunk of their consumers to the competition, they now have to compete with Nintendo, directly, in their main market that they have dominated for decades.  

And by biting the bullet on graphics and power so that their hybrid can have a chance to reasonably compete, putting theirs and Nintendo's systems at the same level, all of the 3rd party developers who used the difference in power and tech between Sony and Nintendo's systems as a reason to justify them shunning Nintendo's system and sticking to Sony's (and Microsoft's), no longer have that excuse.
Unless, of course, they decided to partner with Microsoft and develop exclusively for them, which I can see some of the Western 3rd party companies doing. However, it would be insanely idiotic for the Japanese ones. Which means, we could see games like a mainline Final Fantasy title, which have been exclusive to Sony consoles for so long, make a return or appear for the first time, on Nintendo's systems.

So, not only would Sony lose the advantage of stronger hardware, but the extra 3rd party support that comes with it. Which leaves it down to the one and biggest deciding factor of them all, 1st Party Exclusives. And THAT'S where Sony has always fallen short with their handhelds and why the odds would be so stacked against them if they decided to go the hybrid route.

In terms of quantity, I think Sony's amount of 1st party IPs is actually the same as Nintendo's. Hell, in terms of diversity and variety, Sony's might even be better. However, in terms of popularity, recognition, and brand power, none of them, NOT ONE, can come even remotely close to Mario or Pokemon, ESPECIALLY in Japan, which is the strongest and biggest market for hybrids/portables and Nintendo's market. There, you can also add Animal Crossing, Tomodachi, Splatoon, and Smash Bros. to the list. 

Conclusion:
With all of this taken into account, I think a PlayStation Switch would have a small chance to succeed and the risks would be too big. And with the position Sony is in right now, I don't think they should even bother. The best thing Sony can do is to just keep doing what they're doing. If it ain't broke, don't fix it.

Its not just the hybrid part that makes the Switch a success. Its also how Nintendo is combining both there Home Console and Handheld Division into one.

That means developers will now focus on 1 system.

Think of it this way:

PS4 : sold 70M so far
PS4 with play on the go option: Will it sell less than 70M?

No i don't want that. The PS4 is flying and we are getting more awesome games than ever. It has hit a sweet spot.

They can try that when I am to old to game and care lol

I'm sure the PS5 will be built to be VR ready, with the only extra purchase being the headset itself ($200 max). I wouldn't be surprised if the DS5 plays double duty; a traditional looking gamepad that splits apart and has built in motion tracking for VR.

I don't know why sony would bother copying nintendo all of a sudden but I'll go along with it. If sony supported the console with games, it will likely do well.

No ,it would not succeed.

I think Sony is in a funny place though. Making a hybrid will cause Microsoft to have the only super powerful machine in the market. They will dominate the high end of the market. If Sony goes after Microsoft full force then now Nintendo owns the entire low end market. So Sony is fighting a two front war here. If Sony is lucky Microsoft will continue to decline and they can knock a competitor out. Ether way it will be very interesting on how Sony will react to the Switch. This isn't like the Wii. You can't just add portability. Generation 9 will be an interesting generation.

The only way I see a Sony handled working is if it shares the same Architecture, OS, Software, and Services as the home unit.

Sony does not have the resources to have two different platforms, with their own OS, and Software library.

If Sony makes a PS4 Portable on the 7nm PS4 chipset, they will have no problems in the mobile/portable space.

The PlayStation 5 ecosystem should have a Portable and a Home unit from the start. Let people choose how they want to engage with PlayStation. Shared library, shared OS, shared Network Services, and shared Software. Add in 5G and the ability to make it the one device that goes everywhere you go, and they will continue to expand their ecosystem and thrive for many years to come.

The problem is that if they DO go that route, ninty will be on thier rails with probably a stronger console within a year or so, cortesey of nvidia being in the lead for powerful mobile chips(the only one who has comperable chips is apple), considering that it would take a couple years of tech to sucessfully make a backwards compatable ps4p at a round 400 dollars.

They will probably lose 3rd party exclusives to ninty since power levels will be similar.

They would be leaving MS to dominate the high end console market.

Which means, in the end, what will matter is first party exclusives. And to be blunt, ALL of sony's first party COMBINED would barely match zelda in terms of popularity, and zelda is only a 2nd tier franchise in japan. Pokemon, by itself, has ALWAYS been the MAIN driving factor in ninty's dominence in the handheld market. And sony can't hope to match that. Not when sony's ip recognition is equal to metroid at best, and metroid is arguably the weakest franchise in ninty's first party lineup.