I voted "free patches with meaningful improvements", not because I think they will be common, but because it's the only option I see happening at all. I don't think publishers will be able to opt out of system-provided BC with the previous generation, as long as no changes to the game code is needed (which seems possible).
On the PS5, I expect it to work much the same way as the BC in the PS4 Pro - very good unenhanced compatibility provided by the system for all PS4 games, optional boost mode that provides moderate enhancements due to higher CPU/GPU clocks and faster storage, but no game-specific enhancements and with theoretical compatibility issues due to timing differences. With the HW on its own providing less compatibility than the PS4 Pro did, some game-specific workarounds may be required under the hood. Some obscure games might require but not get those, so overall compatibility may be somewhat less than 100%.
Publishers could still publish remasters that provide more enhancements than boost mode, including higher-resolution assets, re-baked for the enhanced engine, etc. And of course do full QA to detect and fix timing issues potentially existing with boost mode. Such remasters would be full-sized, not require the original game, and therefore not be perceived as "paying for BC" by reasonable people. Remasters would sell less because of competition with the BC version, but for people not already owning the game, I suspect many would pay up for the best version. (And mysteriously, heavy discounts for the digital PS4 version would no longer be a thing, so less competition on that front.)
