No other political parties tend to have a following that can defend the parties on the basis of argument.
I don't think that is true at all. I think all, or certainly most, parties have a major block of supporters whose support is based on nothing more that 'I've always votes Tory/Labour/SNP etc' (delete as applicable). In many cases this isn't based on any kind of actual assessment of policies, rather on a kind of broad ideological mood music (Labour are for the working class/Tories help people get on/I'm for independence) rather than detail - or based on rather crude assessment of 'leadership' - Kinnock (Welsh windbag), Miliband (can't eat a bacon sandwich), Hague (wears baseball cap round the wrong way).
So sure there are plenty of people for whom Corbyn is a kind of personality cult, but he's not alone in that (remember Clegg-mania). Actually given that his politics are somewhat distinct from what we've been used to I actually think there may be rather more people than you care to imagine who are energised by him, not on personality, but because they actually see someone finally leading a major party whose politics align with their own.
Don't forget that I am no fan of Corbyn and left the party because of him - but I know plenty of people in the political wilderness since Blair who now have a political home (based on policies not personality) back in the Labour party.