No way.
Playstation don't need to copy or create "insert IP" Killers. They already have a superior pedigree in several genres and don't need a similar experience.
Ensuring the pedigree and quality of the gaming experience is the absolute priority. You look at the last 10 years of releases and Playstation dominated the market and set a very high level of excellence with several games of the year and nominees, it even got more awards than the other 3 most awarded publishers combined*! Sales also show this, as many PlayStation exclusives are selling over 10M copies, or even closer to 20M. The results in the PS4 generation awards and sales are proof that Playstation is on the right path and doesn't need to do "similar experience".
On the other hand... if a studio in the playstation family has the desire and absolute confidence that they can create something similar, but of superior quality, it's "okay" to make a fps RPG in the Western mold. For example, Guerrilla could try to make a new IP with multiplayer elements and a Fallout-like experience using the Decima engine.
*https://www.gameawards.net/