glibc really doesn't want to be statically linked so if you go this route your option is to ship another libc. It does work but comes with its own problems— mostly revolving around nss.
And NSS defines how usernames are matched to uids, how DNS works, how localization works and so on. If you're changing libc you need to ship an entire distro as well since it will not use the system libraries of a glibc distro correctly.