D&D 5E Should 5e use monster stat blocks for animal companions?

[CapnZapp]

I'm sympathetic to the argument that some things are in place because 1) the general gamership wants it some way and (and this wasn't stated previously) 2) perhaps the general, non-optimizing gamership hasn't had a problem.

However, when was the generic way tried in the past?

I'm thinking of a series of polymorph spells. Not sure if that was Pathfinder or perhaps Rich's houserules over at GitPG...