Thanks for this writeup.
What goes wrong when trying to build with gcc? Although I prefer clang over gcc, I don't know if there's a great path forward here. autoconf (as a Gnu project) is unlikely to stop preferring gcc. There are thousands of autoconf-using source distributions, and for each one of them to add its own per-platform decisions about the default compiler would be inefficient and unreliable.
Changing shlib.conf to use $(CC) -shared is probably good. I note that NetBSD uses LDCOMBINE='$(CC) -shared' (no other flags); I don't know if there's a reason for the discrepancy with Linux platforms.
I would ordinarily expect that if a platform implements libm functions in libc that it would leave behind a stub libm, since -lm has a long history. But a configure test is appropriate now that there is an example of a platform that chose not to do that.
The PKINIT LibreSSL incompatibility comes about mainly because LibreSSL defines OPENSSL_VERSION_NUMBER to 0x20000000L, essentially declaring itself to be OpenSSL 2.0, while having no interest in maintaining compatibility with OpenSSL's API changes (or even some of its pre-existing features, such as CMS). People have written PKINIT patches to work around this, but it's really inelegant, and the rough consensus has been to push back against LibreSSL's bad practice here rather than accept it. I think it would be reasonable for configure to detect whether libcrypto comes from LibreSSL and disable PKINIT.