The problem is they also have problems which motivates people to statically link.
I remember back in the Amiga days when there were multiple libraries that provided file requesters. At one point I saw a unifying file requester library that implemented the interfaces of multiple others so that all requesters had the same look.
It's something that hasn't been done as far as I am aware on Linux. partially because of the problems with Linux dynamic libraries.
I think the answer isn't just static linking.
I think the solution is a commitment.
If you are going to make a dynamic library, commit to backwards compatibility. If you can't provide that, that's ok, but please statically link.
Perhaps making a library at a base level with a forever backwards compatible interface with a static version for breaking changes would help. That might allow for a blend of bug support and adding future features.