There may be an element of this. But it's also the case that the older comedian is either at the end of career, or has made enough money, and does not care about upsetting the delicate students.
A younger comedian is less likely to wish to annoy what is a large part of their target audience, and still cares about their future career.
But a younger comedian is also more attuned to the "triggers" that will cause problems and effortlessly avoids them. An older comedian has to pay more attention to what they are saying to avoid blundering into a taboo topic that, in their day, would have passed unremarked.