None of the OP's suggestion fix the problem both the PSP and the Vita had: weak first party lineup that was often at odds with the console line up. Nintendo handhelds have long been "first class citizens" while the PSP and Vita got spin-offs made by B-teams.
Slight detour, but that idea that Nintendo treated its portables as "first class citizens" while Sony always put its low-tier teams on portables is IMO long-standing BS. When you look at them side by side, they're pretty similar. Granted, some of the massive studios like Naughty Dog and Santa Monica have not coded their own games, but Guerrilla, Polyphony Digital, ClapHanz, Media Molecule, San Diego and others made games in-house on PSP or Vita, and the "B-studio" teams they tended to put on portables were good studios, some of which (Sony Bend and Tarsier and Ready at Dawn) are now top teams. Nintendo meanwhile gets credit for its own creative heads "making" portable games, but when you look at the credits, it's a top-line producer with a notable name but then the core development staff are way down the line or still cutting their teeth. Nintendo produces a lot in-house at its EAD office, but it has also farmed out lots and lots of work to Artoon and AlphaDream and Natsume and ND Cube and the like. Retro ported a DKC game, but when it comes to original productions, they're too big with their console work and let minor studios like NST make the portable version. And it's hard to consider the portable games "first-class citizens" when the budgets for portable games from Nintendo are clearly fractions of what the publisher pays for equivalent console products (albeit at lower prices, but that's a self-fulfilling situation,) whereas while Sony never over-invested in portable games either, the visible production value in money it poured into products such as the GoW duo and Uncharted GA is on a higher scale than what Nintendo has ever spent on any given portable game.
They generally have a similar approach to the business of producing portable games; the schedules that Nintendo affords its development team and the franchises it has in the roster, however, make for drastically different results.
Although Nintendo doesn't maintain a lot of continuity across its franchises, few gamers consider the portable versions of its games to be "canon", and as much as I love portable games (and personally hold Zelda: Link's Awakening as my favorite Zelda), it is clear to see that every portable game is a smaller and less valued title than the equivalent game on console from the same era. Mario and Zelda and Metroid and Fire Emblem have never been content with the GBA/DS/3DS games they're getting, they've always used them to bide their time for the "real" games that eventually come to the home platform.
I don't think Sony ever understood handhelds. Their efforts to me were more of a portable, semi last gen console. Literally the same experience you had already had in the palm of your hand.
Nintendo always get the 'gimmick factor' of the hardware right, then they have a really diverse game library which includes many games that are a perfect marry for that type of device. I always found these to be absent on the PS portables, or mostly absent.
I'm also calling BS on this commonly-held belief, that Sony just made lots of ports and console wanna-bes while Nintendo had the perfect formula for what makes a portable game. (That said, I am reading more global sentiment into your words than you probably meant.)
Sony had a wide variety of games on portables, from big epic console-quality games like Daxter and KZ:M and the sports games to bite-sized things like Patapon, LocoRoco, Little Deviants, Smart As, etc. They had staples like sports games and racing games and puzzlers; they had multiplayer games like SOCOM and Unit 13 and Buzz; they had play-your-life-away games like Wipeout and TM:HO and Lemmings that could be played a little bit or for hours and hours. Most importantly, both of their portables had a rest mode feature (thank god that now every platform has that; it was far and away the best thing about being a PSP and DS fan in that era of painful loadtimes) which made every type of game from the massive epics to little time-wasters as bite-sized and easy to put down as need be.
If Nintendo had the perfect formula all along for exactly what a gamer wants in a portable, we would be seeing something else besides the console-sized Zelda and Mario Kart (and soon Splatoon and Mario) being played on every train and at every park bench and in every DMV line. As is often the case, any approach can be the wrong thing to do in the gaming business until Nintendo comes along and proves that it can do it right.
It was imo Microsoft's best efforts into hardware and UI. Had my HD since launch until it got stolen a few weeks ago, 7 years that thing lasted
