It's hard enough to follow this topic for many people that want to keep updated. The fact that you have to spell out "please use SHA2-512/256, but not SHA2-512 and not SHA2-256" is mind-numbing.
"It's really SHA2-512/t where t has a value of 256 and that means that it's SHA2-512 truncated down which alleviates length extension attacks." Just typing that sentence gave me a headache and I have no real idea if it's right or not.
Adoption would be easy if communication was easy. As it is, it's a PITA to even have a short conversation on the subject.
That's what I'm trying to articulate. Hashes aren't MACs.
This is partially my fault, for playing loose with SHA-2 512/256 vs "The Prefix MAC built on SHA-2 512/256".
Again: I think we should just call that SHA-2-MAC. It's an unambiguous name that couldn't mean anything other than "truncated SHA-2 512 used as a prefix MAC".
Seriously, if you care that much about the name, rename it; Even systems that use SHA-3 use HMAC (SHA-2 is perfectly safe, no matter what variant you use, in HMAC). Name the prefix MAC (an idiosyncratic construction) that uses SHA-2 something specific.
The SHA-3 advocates have already conceded this point. They don't call SHA-3's prefix MAC "prefix MAC"; they call it KMAC, which is a specific construction.
So all you have to accept is that there's SHA2MAC --- which, like KMAC, is not simply the hash function, but instead the optimal MAC construction built on the hash --- and then define it as the prefix MAC built from SHA2-512/256.