It's not a technical problem. All distro package managers allow for parallel-installed libraries one way or another.
What's necessary for your distro to actually ship multiple versions is someone stepping up to actually maintain the thing, dealing with bug reports and monitoring security issues.
For libraries with many users that happens all the time. See the parallel packages for OpenSSL 1.0 and 1.1 in most distro repositories. For less popular libraries it's often easier to just patch all users and only ship the most recent version.
Nowadays LLVM seems firmly placed in the first camp, as patching programs to work with different LLVM versions can be a lot of work and there are quite a lot of them.
Looking into the Debian repos, you find packages for LLVM 3.7, 3.8, 3.9 and 4.0, in addition there's even a 5.0 pre-release snapshot. It's similar with Fedora and probably other distributions.