Does anybody know if any ATC training system has anything like CRM training nowadays?
Yep. Its called TRM (team resource management) and its modelled on CRM. Its a part of the initial course at the college i think and everyone else got sent on a course.
As for sims v live traffic. A sim cannot (at the moment) replicate live traffic in any environment be it tower or radar. Live traffic is too dynamic to be replicated by the psuedo pilots in the sims, they do a fantastic job but can only get the trainee so far. After that the trainee has to see live traffic so experience the oddities.