The evidence is anecdotal ... players whose careers are affected by this seem to just fade away ... they sign for lower league clubs or slip out of the game with little or no fanfare. Supporters might not notice, or turn around and say they 'found their level' like was said about Rory McCallister, and indeed some of it may be just that, in the same way as you might only get 1 or 2 out of 100 academy kids reaching the first team but burnout does happen. You say Rangers did it - very true, but both them and Celtic cherry pick youngsters from all around the leagues not just their own academy so I would argue the stats there may be skewed.
Best example I can think of in world football of burnout like this would be Freddy Adu, but like I said, i see it myself at Toronto over the last two years especially. Luke Singh was - in my opinion - almost ruined by our former boss after being expected to play in the first team every week. He got hung out to dry for a poor performance after 6 or 7 weeks as he wasnt mentally ready to play every week, and his head went down. He was dropped after that last appearance and we havent seen him since. He is now on loan at FC Edmonton in the tier below MLS. Our new boss Bob Bradley has a lot of youngsters in the squad, and although he is trying to manage their minutes more closely, has little alternative but to rely on youth a lot as he rebuilds. That comes with challenges of enthusiastic but inexperienced performances, as well as the risk of burnout. It doesnt take much to shatter a young player's confidence.
Bottom line is I am not saying we should not play the youngsters, but lets manage our own expectations. Every player cant be Ryan Christie or Daniel Mackay and we are more likely to see half a dozen who are competent and grow into the role more slowly - or not at all. I was impressed with what I saw of Hyde towards the end of last season so provided we have coaches who will mentor and develop these types players that's fine ... but its not the answer to all our issues or budgets.