For example, Horizon: Forbidden West uses a custom physics engine that started out as one of the core dev's fun side projects: https://github.com/jrouwe/JoltPhysics
Physics engines (at least game quality physics engines) are starting to drift in to "solved problem" territory and there's enough literature now that you can get something reasonable going yourself after doing some weekend reading.
Edit to add: Godot has had its own engine available for a long time, so it's not a totally new effort. It's a heavy refactor and a large improvement but the bones for this were laid years ago so some of that technical debt you're describing has already been paid down.
Additionally, there are people in robotics who like to say that simulators are like lightsabers, you haven't become a true Jedi until you've built your own, so there's a lot of home grown physics simulators in robotics.
[1]: https://en.wikipedia.org/wiki/Featherstone%27s_algorithm
https://bevyengine.org/assets/#physics
Forgetting about extensions, though, I see your point and almost agree, but Godot has shown that they will put in the work to improve their project, even if that means removing features like they did with visual scripting. Their physics engine will definitely be rough at first, but based on their past work, I believe they are willing and able to maintain it.
It sounds like it's got bugs that need fixing either way, so at least for their own engine they're not reliant on anyone else to get those fixes out (or have to use hacky workarounds as would most likely be the actual fix).