It's not the only reason. But it is an important one. It would partly sway me, to think of no uni fees.
I, myself was one of the last students to experience uni, without the extortionate fees, all those years ago!! 
The other thing is that these new voters have not really known a labour government. They may not remember Blair that much. Cameron has been in power since 2010, so Tory since then. That's 7 years, so quite long. In politics.
These voters won't remember how young and exciting Blair was. But later we remember Iraq and the fact he left us in such deficit.
Now I am not a Tory fan. Nor Labour either. Wasn't a Blair fan either.
But one fact that the last 7 years of Tory rule can't deny, is that the austerity measures have reduced the deficit significantly.
Which is at least ONE good thing.
I'm just saying that these voters do not have much experience of previous governments, so may not realise that Corbyn may not be all that 'glitters, ISN'T gold'?