wouldn't it be possible to still run them with some LD_xxx magic where the c++ shared libs are put in some folder and loaded from there? (It's really userspace problem).
Yes - I've done that to produce more portable Linux binary installers where static binaries would have caused other problems - I tested it for backwards compatibility, but hopefully it will also improve forward compatibility.
One problem that you encounter if you do that is that glibc has an option to disable support for older kernels in exchange for better performance, so you lose backwards compatibility unless you are very careful about how you compile glibc (it fails with an error that the kernel is too old).
Linux can run statically compiled binaries from 1993, but not the Firefox binaries from 2006.