imagine how many people would switch to digital only, wow.

It would be nice, but Sony's record with support is not good, so no

Wouldn't that mean this is the perfect time for a handheld that can play that new library of handheld games?

At this point even I would have a hard time getting a Vita Pro. Without 4G, PS Vue, PS Music, PS Video, PS Now, Communities, The Activity Feed, and the rest of the PSN features I would not have any interest in it. 

If Sony wants to re-enter the Mobile space they need to dump Xperia and Android and deliver an Ecosystem built around the foundation they have layed with PS4. Unified OS, Unified Services, Unified Apps, Unified Games Library. That is the only way they can re-enter the Handheld space and ever have any hope of carving out a small segment in the Mobile space. Vita and Xperia are dead platforms.

The only Sony's handheld that could sell, would be PS4 portable. And if that's even possible to make, I'd buy it.

Sony tried to compete with Nintendo in handhelds and got smocked like a salmon. They learned their lesson and are sticking to what they're great at, home consoles. Any idea of a handheld is just wishful thinking.

I got a PSTV and I was excited to play my Vita games on a TV. Turns out, I didn't enjoy it much at all. The games were good for portable but not so hot as a full experience, in my opinion. Better performance wouldn't change my opinion.

The biggest problem with the Vita wasn't power. It was a pretty dang powerful handheld when it launched. The problem is support. At this point Sony is not releasing games anymore for the system and big thirds moved on, and also the small thirds are also starting to move on to support the Switch. A new piece of hardware does not interest me if you don't give games to it, if they release a new handheld and give the same support they gave the PSP, then you can consider me as a costumer.

I can only think of Monster Hunter but that had a Wii U game. 

The major problem is power consumption/battery technology and without a grand leap forwards in those areas it's probably not a good idea.

With 7nm manufacturing it might be possible to get consumption (including additional components a HH needs, like screen/speakers etc) to about 50W (the PS4 Slim has a peak draw of ~90W and it's APU is made with the 16nm process). In comparison the Switch is at ~9W max consumption in hh mode and already is critized quite a bit for only offering a bit more then 2h battery life in demanding games.

A makeshift solution might be to include ~30min battery life in the hypothetical PS4portable itself and shipping it with a power bank that you can wear on your body without too much of a hassle, but I doubt the public would be all too receptive of that.

I would buy just for collection purposes probably.