In my opinion you can send ATCOs or pilots anywhere (center, twr, fam flight, etc.), it doesn't worth too much if the person is actually not interested in it and not motivated to know a bit more.
I guess we've all seen it way too many times, that there're a lot of ppl only interested in getting the paycheck in the end of the month and not really in the rest. They do their job, but noone should bother them with things like why is this and this happening if I do that?
Having said that, I absolutely agree that there should be better communication between the two sides (and also between ATC units) and we should organize some training days together for the benefit of all involved. Every single time I go to another center, to a cockpit flight I learn something new. And in the best case the other side learns something new as well, since it's not only one-way talking, but a discussion.
When I talk to pilots they say during their emergency simultations everything seems so real except ATC. How about our emergency sims? Everything is so real except the pilots part? Sim pilots are sometimes very good and put an huge effort into making it as real as they can, but they can never reproduce the reaction of an actual crew. Why don't we use our "refresher training" days to get together and do these simulations together?
It wouldn't change the world for sure, but I'm positive it would help at least a little bit...