What does transferring have to do with it? At that point they have already competed and lost. Most starters don't leave. But that is different than being afraid to compete.
Feeling entitled is not the same as afraid to compete. If I am up for two coaching jobs and the job at the school that doesn't have a great history offers me more money so I take that job, doesn't mean I am afraid to compete, it means I want more money. I can negotiate with the other school, but in the end I am going with the money. Same with athletes, just because they go to a "lesser school" or go with the school that guarantees playing time, that doesn't mean they don't want to compete, they just like the safety of the guarantee.