Yes it is. But they need to divide their resource to make another gadget.
For now SCIE are full with PS4 , PS VR, PS Now, PS Online, Games Studios and future PS5 . Just let they focusing on PS5 first and let PS brand getting more bigger. Once the time comes, i think they will making it in the end.
SCIE doesn’t need to fully support it. Sony already has Forwardwork that is dedicated for mobile.
It’s their phone division that needs to do it. Build up a studio for it. Like Sony Music they are the ones handling Fate on mobile.
Or outsourcing from 3rd party devs.