Whilst I'm not sure what you mean by 'top airlines' I would use an example of a very large UK airline, particularly famous for it's colour. They routinely have new intakes of pilots with a minimum of just 500 hours 'in a multicrew environment' which can include military. They have had no ATC training at all (I'm happy to be corrected but I don't think any airline provides this).
Frankly in this scenario, I'd be struggling to fly the aircraft let alone deal with a busy TMA sector, or a packed LHR holding point before 'maxing out'.
Thanks to changes in training and requirements both ATC and pilots know less and less about each other's jobs. We can make up for this with familiarisation but convincing anyone senior to part with the money or time can be tough. I routinely do this sort of thing in my own time and/or off my own back. I am not cool, but regardless of who you believe should be providing these opportunities my professionalism will not be dragged down by a lack of others presenting them to me.
