The problem with Sony making a handheld is that it will run into the same problem that Nintendo did: Having to support two systems. No company is exempt from that in today's market. Look at how long it takes Sony's games to arrive for the PS5 now. Imagine if it had to develop for a PSP 3 as well.
The only way that Sony could realistically compete with Nintendo in Japan would be to make the Playstation 6 a hybrid system and that would critically limit the company's mantra of delivering a cutting-edge home console with its next entry. Why on earth would Sony want to fight an uphill battle against Nintendo in Japan when it can do what it does best, which is make a very western oriented console for its biggest IPs, which also appeal to the west: Spider-Man, God of War, The Last of Us, Uncharted, Horizon, Helldivers, etc.
I realize that it is very unfortunate for Playstation fans in Japan that Sony has taken this route, but in the long run it is all the better for it when you consider how Sony fares now on a global scale. Plenty of room in the western gaming market for both a "Playstation" and a "Switch" to not only coexist, but for both to thrive. But ultimately, it does result in Playstation giving up competing with Nintendo in its home country.







