This is a big forwards-compatibility risk. Suppose glibc adds a new symbol, and then a GPU driver adds a dependency on that symbol. The user wants to run an old executable with the updated GPU driver (maybe the old GPU driver doesn’t support their GPU). Normally, this would work fine: the user has to use a new copy of glibc, which will be compatible with both the new GPU driver and the old executable. But with your approach, the GPU driver is forced to use the glibc reimplementation which has been statically linked into the executable. Which, since the executable is old, can’t possibly implement the new symbol.
The same issue would occur if glibc adds a new version of an existing symbol and then the GPU driver is recompiled. (Or, for that matter, if a GPU driver adds a dependency on a symbol which glibc has always supported but which isn’t in the subset that you reimplemented, though in theory that could be solved if you reimplemented 100% of the symbols.)
Yes this is just asking for trouble - and all it does is solve a problem that doesn't really exist. Just dynamically link against the oldest glibc you want to support. Its annoying that Linux toolchains don't have built in easy mode support for that but its much easier to deal with than this thing will be when it breaks.
It's also not just new symbols, the loader semantics also aren't static and new enough libraries may not support older semantics - e.g. the loader used to use DT_HASH entries for symbol resolution but now they are no longer present on all distributions.
This means the user will update the binary with my program and continue using it happily.
I'm not offering a silver bullet, but the approach I've implemented is much better than what the industry currently offers.