Yes but we are talking about a catalog of 10000 games or more. What about licensing/testing for example.
Backward compatibility and emulation have been done numerous times throughout the years. Sony has been quite proficient at both of these in the past. We shouldn't be treating it as a lost art. PS2 and PS3 had excellent compatibility out of the box, and even the PS1 emulators on PSP and PS Vita were extremely well done.
I am sure many studios would not be happy to see their games being played without them making any profit.
I didn't hear many complaints from studios for backward compatibility on PS2/PS3, Wii/Wii U, or Xbox One.
If they want to sell new copies of old games, then they can make them available as digital downloads.
People who already own the old discs aren't as likely to repurchase the games as digital downloads anyway. Since they've got the old discs, it's highly likely they also already own an old system that they could play those games on. Might as well enable them to play those games with improvements and QOL features on new hardware. It would be a selling point for the hardware, and might encourage those people to buy digital downloads of other back catalog games.
What about games from studios that don't exist anymore.
Same as any other game. Enable existing discs to be playable on the newer systems, which would require no new licensing whatsoever. If some company wants to publish a digital download on the online store, then they can track down and negotiate the rights. This has already been accomplished by numerous companies on numerous platforms, including Sony during the PS3 era.