No idea why the glibc can't provide API+ABI stability, but on Linux it always comes down to glibc related "DLL hell" problems (e.g. not being able to run an executable that was created on a more recent Linux system on an older Linux system even when the program doesn't access any new glibc entry points - the usually adviced solution is to link with an older glibc version, but that's also not trivial, unless you use the Zig toolchain).
TL;DR: It's not static vs dynamic linking, just glibc being a an exceptionally shitty solution as operating system interface.