I don't think it is 'simple as that' that the young supported Corbyn because of his promise to scrap tuition fees.
Obviously that was/is important to them, but they are not fools. My two were both fans, and yes, they were idealistic, as befits their youth, but they listened to far more than that one promise. My son (the elder of the two) is less enamoured of him now, but my daughter often says that she wishes he were still the leader.
I think that maybe there should be a split. There is clearly a chasm between the right and left of the party, and there is nothing to be gained by one side sniping the other instead of concentrating on what needs to be done.
The LibDems are all but washed up, and historically they took votes from the right of the Labour Party, so there could be room for a joint effort there, leaving the left to offer their agenda to the voters, and neither side would have to temper their message to suit what is considered by others to be electable.