The question is less 'should they?' and more 'can they?'.
Seeing powerdraw and heat contraints of a mobile device they have two possibilities:
1. Go with a mobile chip based on ARM that is specialized for mobile needs.
2. Wait for another die shrink and have AMD design a X86 based SoC for them.
Regarding the 1st option, the Switch is already using the most powerful mobile chip currently out in the market. Yes Nvidia has since unveiled and released the successor chip that is twice as powerful/half as enery consuming, but so far it's only used in 600$ dev kits and cars and no consumer version has been released.
And even that chip would require serious porting/optimization for PS4 games to run seamlessly, since it still is a weaker chip on a diffrent architechture, with less bandwith. It would not be a smooth process and people would likely have to rebuy the games, or have them digital only.
That leaves you with option two. Pray that nothing catches on fire basically. X86 just isn't where ARM is when it comes to powerdraw/performance. The PS4 Slim draws 130W with a 16nm architechture and is bigger and thicker than a conventional 13'' laptop and heavyer than my late 2011 macbook pro, wich at 2kg is quite the dead weight to lug around.
Compare that to the Switch, wich at 400g and a size of 10+22 cm (joy-con attached) was criticized for not being small and protable enough and for it's weak battery life even though it only draws a MAX enery of 39W while docked and less than that in HH mode.
Even with a 10nm die shrink and assuming 50%+ less powerdraw the PS4 isn't even in the ballpark. A 7nm die shrink woulf get you closer, but good luck getting that within the PS4 lifespan. It would be so expensive and such an extensive redesign for Sony, that it just isn't worth it imo.







