I think a lot of people are missing the big picture here which is that Nintendo both captured and perfected the handheld market... This isn't an opinion, just the way it played (and with now over 5 decades of focus, beginning with the Game & Watch [..which also went dual screen..] it isn't really a surprise!).
The DS released at a the same time as the original PSP (I owned and loved both consoles), but whether it be Ninty's ~24 years in handheld at the time, or their extra features (some will say revolutionary, some will say gimmicks) they still outsold the PSP almost 2x over. The DS didn't outsell the PS2, which in the same era literally revolutionised the home console market with raw power. The PS2 brought all of the successful partnerships that the PS1 attracted, plus all of the biggest 3rd party developers leading to the biggest selling console of all time (which was only tailed shortly by the DS).
The DS had a backing of decades worth of handheld development. (Arguably, they also revolutionised the mobile game market with intuitive touch screen controls).
At this time major developers were happy to throw funds into developing games for a handheld with such immense sales. (Biggest downside to this was the absurd influx of shovelware, which was exacerbated by the introduction of the disguised turd that is casual mobile phone games, which has continued to this day).
The PSP had the backing of Sony's biggest third party developers like SquareEnix, Rockstar and Capcom (as well as SCE), it also had exceptional sales but I personally think that the cost of development and a smaller return compared to Home Consoles, even with the PSP, Sony was still looking to 'out-power' Nintendo which led to bigger losses due to development costs.
In their continuation of revolutionising of (or just plain fucking with) the market, Ninity produced:
The underpowered Gamecube
The underpowered, but revolutionary Wii.
The (maybe only gimmicky, but better powered) 3DS
The (at the time, still underpowered) WiiU
At at the release of the WiiU, the handheld market was mostly owned by Nintendo. They had carved out their niche and planned for their next step into weirdom, which was the amalgamation of:
Their centuries old brand with obscure but popular ideas,
Their underpowered home console, and
Their dominance of the handheld market
This eventuated in the Switch, which has absolutely dominated both the home console and the handheld markets in this generation (call it a hybrid or whatever, but it's still getting releases of brilliant games without a care for the latest AAA releases on Xbox or PlayStation consoles).
I think Sony would be fucking insane to attempt to develop some sort of true handheld device ala the PSP in this time, and to attempt some sort of 'tuned down' version of a PS5, or a 'suped up' version of the portal will only lead to something quite underwhelming. But I don't know, it would be exciting to see a revival of the good old console wars of the 90s, maybe it's something that doesn't exist anymore with the current climate where developers are more revered than the consoles the games are on...
...forget it Sony, just bite the bullet and put your first party handheld spin-offs on the
Super Switch.
Sorry... This started off as a reply, which turned into an almost opinion piece , which I was like (do I just make a new thread?) but didn't feel it was that important, even with all the crap I just wrote....
I'll just leave it here