I object to the notion that SHA-3 and Blake2 are "modern" hash functions and that SHA-2 isn't. SHA-2 remains a first-line hashing recommendation among crypto designers. The Noise protocol framework, for instance, includes it, as does Nacl; the authors of both of these systems had hashes available that didn't have length extension.

If I had to rank those three hash functions, SHA-2 wouldn't be in last place.