Good counter-points, everyone.
I suppose from my point of view what we see with centrist New Labour is a lot of people feeling disenfranchised. Corbyn has motivated a significant number of people who were otherwise detached from politics. Those are people who - for the first time - heard the leader of a mainstream political party saying the things they wanted to hear. If they lose that, where do they go? Greens? Perhaps, but I doubt many people see the Greens as a party of Government. Lib Dems? They've already committed political suicide and I can't see many of the leftist youth forgiving them for their coalition compromises in a hurry.
As I said, Labour under a centrist leader will struggle to genuinely oppose the government. Labour fractured under a continued Corbyn leadership are basically useless, but Corbyn himself at least stands properly opposed to the Conservatives on most issues. Labour candidates are selected by their local parties, so actually the MPs being out of touch with their party grassroots IS important - they could easily be deselected at the next election if the whole mess rumbles on, and what they're currently doing is turning round to their own party members and saying "I know we said you could choose the leader, but you got it wrong, so let's try again, shall we?". Yay, democracy
And of course, you've always got the risk of a full on party split if Corbyn wins a leadership election - would those 170+ MPs who have no confidence in him resign the Labour whip and form their own parliamentary party?
One thing Leadsom's withdrawal has done is compounded Labour's woes. The Conservatives are definitely better at keeping their discontent quiet, and showing a unified face, whether they believe in their current leader or not. They'll put the knives away in public, look like a strong party, and the lack of uncertainty is already starting to see the pound recover slightly against the dollar, which they'll no doubt claim is due to their good management of the situation (ignoring the fact that aside from the last week it's still at a 30 year low). Strong Conservatives, and Labour in disarray. It's just like the first 15 years of my life...!