[libc++] Revert "Protect users from relying on detail headers" & related changes

This commit reverts 5aaefa51 (and also partly 7f285f48 and b6d75682,
which were related to the original commit). As landed, 5aaefa51 had
unintended consequences on some downstream bots and didn't have proper
coverage upstream due to a few subtle things. Implementing this is
something we should do in libc++, however we'll first need to address
a few issues listed in https://reviews.llvm.org/D106124#3349710.

Differential Revision: https://reviews.llvm.org/D120683