OK so let's say it's "possible".
When? This year? Next year? In 5 years?
There are OBVIOUSLY multiple challenges that, while not making it impossible, make it highly unlikely.
Battery.
Cooling.
Storage capacity.
Physical size.
Various other issues such as controller ergonomics, robustness of the hardware, quality of the screen, marketability, physical game releases etc.
Then once all of those are dealt with you have the issue of cost.
I am sure that if Sony were to develop this thing they would want it to be really profitable since it would literally get less focus than their main home console.
Seems to me that you'd be looking at a massive price tag on something like this.
So while it might not be technically impossible it isn't going to happen anyway so what difference does it make?