1) Black borders on a TV can be corrected by setting the proper output format via >Connected display settings> option in the menu. And if you're too lazy to do that, or to update to a more recent firmware that has that option, then you can just adjust via the tv.
Too much hassle and it overstretches the game making it incredibly ugly. PSP games already look ugly on the small screen it comes with, never mind a big TV with an HD screen.
Yes, that's how laptops work as well. It's a sensible feature, not a cost cutting measure. No other console but the Switch does this.
Nobody fucking bought a PSP Go and even less people bought that peripheral you posted an image of. The PSP Go didn't even support all the PSP games and it was a digital-only device.
It connects to the TV and power supply the exact same way the switch dock does, and when you place the PSP go into this dock, it outputs to TV itself, you can then pick up any sixaxis, dualshock 3, dualshock 4 or licensed PS3 wireless controller and play. Literally the exact same amount of "hastle" as switch.
Except you need to buy a new revision of the PSP (that sold very poorly) and an extra peripheral to boot. And you're still left with the huge problem of playing 272p games on a big screen HD TV.
Plug in, pick up your pad and continue playing, and just like the switch, while you play your system is also charging too, so when you're done you just pick it up out of the dock and continue playing.
5) The PSP got 869 retail released games to date, not including the expansive array of PS1 classics on the ps store either, compare that to the retail releases for WiiU, Just 99 WiiU games released in america, 28 released in europe and 59 released in Japan, and this was a mainline Nintendo console, then we have the 3DS which has just 187 retail releases, 485 if you include downloadable, so even if you combine the wiiu and 3ds's entire retail library it's still significantly smaller than the PSP, so yes, you might not be getting the full force of Sonys main console releases, but you sure as hell wouldn't be struggling to find something to play.
This is utter bullshit you just made up. The 3DS has way more retail releases than the number you posted. Use some common sense man... VGchartz alone is tracking 556 games for the 3DS and there are many more games that they don't have sales data for. The DS sold more than double the amount of software than the PSP and even the 3DS has almost sold as much retail games as the PSP despite having sold 16 million units less. Soon the 3DS will overtake the PSP, it's only a matter of time. The PSP has a lower tie ratio than any of Nintendo's handhelds (or home consoles). It had a weak library compared to Nintendo's handhelds. Even the GBA managed to sell more software than the PSP despite only being supported by Nintendo for 3-4 years.
Switch doesn't have:
All your list proves is the same as what my list proves, they are different devices, from different generations, with different goals and different approaches, that said, a lot of the stuff you are claiming wasn't possible on PSP, infact was, and specifically on the bold section, Ape escape academy 2 supported local 2 player on a single psp, as did a couple other games, but it's a moot point since shortly after release you could buy two PSP's for the price of a switch and do proper multiplayer.
Up to 8 Nintendo Switch devices can connect with each other for local off-line multiplayer (and this doesn't cost you anything, so it does have free multiplayer). Can the PSP do that? You mention one game and I'm not even going to bother looking it up, but it was probably terribly executed (like most things on the PSP). Also all of the things you mentioned are done much better on just about any smart-phone device. And that's exactly the reason why the Vita failed. Smart-phones had taken over and thus there was much less incentive to buy a PS handheld as they were lacking in the games department (PSP sold as much as it did because it could do stuff other than gaming and smart-phones hadn't taken of yet). But in this day and age focusing on that kind of stuff on a dedicated gaming handheld is pointless as people just use smart-phones for all that stuff (just look at the sales of the Vita for proof). Nintendo is correct in focusing on just games with the Switch (and a lot of that stuff can be added later through updates anyway). And who says the Switch doesn't have a fully featured storefront for buying content? Also you forget to take inflation into account and the Switch can also quite easily get price cuts lol...
Also, because the PSP used UMD rather than cartidges, the price of retail games was at an MSRP of $39.99, rather than the $59.99 MSRP of Switch games, sure UMD as a whole wasn't a great idea or all that fast to load from, but the lower retail price of games was nice.
The Switch offers home console experiences on the go, the PSP does not. Therefor a higher retail price is justified. The PSP never got games with AAA production values. The Switch will get these, just look at Breath of the Wild, Super Mario Odyssey, Steep or Mario Kart 8 Deluxe. Besides, I'm pretty sure not every Switch game will cost $60, prices will be flexible.
And then there is homebrew... a homebrew'd PSP is still basically the best portable emulator/gaming machine money can buy.
All in all, the switch is unique on the marketplace currently, but not because of any of the features you've listed, it's unique on the marketplace because the Vita is nowhere to be seen and the 3DS is soon to be phased out, when you consider that tablets with much of the same features already exist, and docking/tv out on a handheld was already done before, then you see that while it's "unique", it isn't all that special.
Unique on the marketplace and unique in general are two different things.
Homebrew is illegal and unofficial and has no room in this discussion... Rampant piracy isn't something to brag about, it's one of the reasons why the PSP has such a low tie ratio.
"The strong do what they can and the weak suffer what they must" - Thoukydides