No, Sony shouldn't was their resources in an internal FPS. This genre is already saturated by other ones, and they can continue keeping them as marketing partners to keep getting revenue from their sales and DLC: CoD, Battlefield, Destiny, Far Cry, Overwatch, etc.
Sony is already doing a great job, better than ever, in the type of internal games they do: narrative focused AAA single player games with stunning visuales, mostly action adventures now in semi -or total- open world games. And combined with smaller highly creative games developed internally or externally.
For their next games they should announce the GoW sequel, Bloodborne 2, Days Gone 2 (and ask Bend to reboot Syphon Filter after it), some new IP by Kojima and if they don't have a big team in Sony Japan working on Silent Hill then to ask the Gravity Rush 2 leads to make an AA/AAA new IP, and ask the Puppeteer and LocoRoco leads to make some small new IPs or sequels of their games.
To let Media Molecule expand Dreams for some years while also working in a new IP, then ask Naughty Dog, Insomniac, Guerrilla, Santa Monica to make AAA new IPs of their genres while having a 2nd team (considering their recent big success they may grow) working on sequels maybe with the help of an external team like the new Sony San Diego studio (maybe this one can make Uncharted 5/Uncharted spin-off with help from ND).
Socom or Resistance are dead for a good reason. The only one I'd revive is Killzone and only if they go back to the Killzone 2/maybe Killzone 3 vibe which unlike the other games in the series had maybe enough personality, style and uniqueness.