As a non-crypto-nerd: How viable is it to make a “safe” OpenSSL, which just doesn’t support all the cipher modes (?) that the HN crowd would mock me for accidentally using?
The modes of operation aren't the main reason people use OpenSSL; it's the support for all the gnarly (and less gnarly) protocols and wire formats that show up when doing applied cryptography.
Progress is being made on replacing OpenSSL in a lot of contexts (specifically, the RustCrypto[1] folks are doing excellent work and so is cryptography[2]), but there are still plenty of areas where OpenSSL is needed to compose the mostly algebraic cryptography with the right wire format.
Edit: I forgot to mention rustls[3], which uses ring[4] under the hood.