I think the devs really missed out on an opportunity by not having followers be your instructor for specializations. That would have been so cool, maybe even get a special personal final quest with just the two of you as a conclusion to unlocking their particular spec. *le sigh*
While I like the idea of this, I don't think it works for everyone. Personality aside in relation to "teacher material," let's just take Cassandra's spec: templar. This is a discrepancy with game mechanics not meshing with the lore. In this case, she would have to have an un-teachable seeker spec since she didn't even know about the method until later on, and I doubt she would be able to replicate it, OR would want to inflict it on someone. And then you would learn templar from, say, Cullen. But that has its own issues as he is reluctant when you broach the issue.
Or let's take Iron Bull's reaver spec. That particular spec fits him as a 2h warrior, in addition to the whole "dragony" thing he talks about. But I'm not sure if he would actually BE a reaver if this were somehow real.
So I think it's complicated and that the writers would have to design it that way from the get-go. I don't think it should be a matter of, "So-and-so has whichever spec, so the follower can teach it to them."
I think this applies to some of the DAO specs as well.
In any event, it is implied that each companion adds something from themselves - depending on the role, we have to go and find a book near each companion that describes the specialization and we can discuss things with quite a few of them, so it's quite easy to RP that they've contributed to Inquisitor learning or honing chosen set of skills.
This is a great way of looking at it and not something I had considered.