Hamlet did, though. I'm not sure what Laertes was going back to France for, but it could have been school. And then there's the three "scholars" in Love's Labour's Lost.
My question is this - how frequently did Shakespeare create characters who were students, and do we think that his depiction of those characters (or his failure to do so) had anything to do with his own experience or lack thereof?
This is indeed a variation on the "If Shakespeare never went to Venice how did he describe Venice so accurately?" question. I thought it might be a little change of pace.