Should they, I dunno. Could they? Yes, but they would have to make sacrifices if they plan to launch it soon.
They would have to use arm and port the PS4 games over.
They would have to downgrade the games to 720p and probably medium settings.
They would probably want to use a larger battery than Switch, which would add to the thickness of the handheld, plus extra cost.
They would either have to use carts, or put a BD optical drive in the dock to transfer games to the handheld (which would require enough mass storage built in to have say 4-8 games on the handheld at all times, increasing the cost of the stock system or due to a necessary memory card purchase do to limited stock storage).
If they waited until 7nm, they could probably use x86, but still play the games at 720p and medium settings, allowing the chip to run between 60% to 85% so its power usage and heat output is low enough.
A PS4 Portable is doable, but the effort to make it happen in the near future, may not be worth it financially. Waiting for 7nm, when PS5 will be getting ready to take the spotlight, would be an odd time to launch a PS4P. Naming it something different, but making it clear that it plays PS4 games and uses PS4 optical discs, would work.
PS1 - ! - We must build a console that can alert our enemies.
PS2 - @- We must build a console that offers online living room gaming.
PS3 - #- We must build a console that’s powerful, social, costs and does everything.
PS4 - $- We must build a console that’s affordable, charges for services, and pumps out exclusives.
PRO -%-We must build a console that's VR ready, checkerboard upscales, and sells but a fraction of the money printer.
PS5 - ^ -We must build a console that’s a generational cross product, with RT lighting, and price hiking.
PRO -&- We must build a console that Super Res upscales and continues the cost increases.
