There's definitely value in the static approach in some cases, but there are some downsides e.g. your utility will need to be recompiled and updated if a security vulnerability is discovered in one of those libraries. You also miss out on free bugfixes without recompiling.
If you require a library, you can specify it as a dependency in your dpkg/pacman/portage/whatever manifest and the system should take care of making it available. You shouldn't need to write custom scripts that trawl around for the library. Another approach could be to give your users a "make install" that sticks the libraries somewhere in /opt and adds it as the lowest priority ld_library_path as a last resort, maybe?
If you require a library, you can specify it as a dependency in your dpkg/pacman/portage/whatever manifest and the system should take care of making it available. You shouldn't need to write custom scripts that trawl around for the library. Another approach could be to give your users a "make install" that sticks the libraries somewhere in /opt and adds it as the lowest priority ld_library_path as a last resort, maybe?