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glibc cannot be linked statically.[1] Compile hello world against musl libc with -static and you get an 8kb binary.

Here's another link which compares musl, uClibc, dietlibc, and glibc sizes, features, and performance.

It says musl's smallest static C program can be 1.8k as opposed to glibc's 662k, showing libc doesn't always have to be big and bloated.