Talking TLS with EC cryptography and the secp256k1 curve
BIP32 uses secp256k1 because BIPs are for bitcoin and bitcoin uses secp256k1. (I feel like Buffy 1.01: "[the reason I'm here now is] because now is when we came here".) The same approach(es) would work for any elliptic curve, with obvious substitutions for ser256 and parse256, and for serp if using a non-Weierstrass form like X25519. 

But TLS in practice requires certificates for authentication keys (or kRSA, no longer recommended and in 1.3 no longer supported) and certificates don't mix well with rapidly or dynamically creating keys, via BIP32 or any other means, regardless of the curve(s) used. ('In practice' because there is an RFC for using raw keys, but I've never seen an implementation, certainly not in OpenSSL.) 

PS: nodejs builtin 'tls' is OpenSSL, compiled into node[.exe] underneath. You can get alternative (pure-JS) crypto including ECC, but I haven't seen pure-JS TLS.