The evidence just doesn't bear out, though. Where are these magical leftwing voters coming from? The Labour Party could win every single Green party voter there is (and it's ludicrous to suggest they would, the Green party has its own identity that exists independently of how leftwing or not Labour is), and would still have less votes than the Conservatives. The SNP are a more rightwing party than Labour was under Miliband and arguably than under Blair, so it's difficult to see how Corbyn helps with that - the issue is messaging, not policy. There's no evidence that non-voters are significantly more leftwing than they are rightwing (they're marginally so, but only because younger people are somewhat more likely to be non-voters), and there's no reason to suppose that Corbyn will galvanize the left-wing non-voters more than he will the right-wing ones to vote for the other side. What's left? Winning TUSC votes? Wow, election-winning strategy right there.
Let's be brutally honest, here: British elections, fundamentally, are decided by a very small group of Labour-Conservative swing voters in a number of key constituencies, and by the media sources they read the most which have a large part in determining their decisions (primarily the Sun and the Daily Mail). Nobody else matters in deciding who takes government. This group of swing voters has shown no real preference for Corbyn over any other candidate, and tend to, as a whole, lean towards Burnham before anyone else (even Liz Kendall, contrary to Cyclops Rock's suppositions).
That doesn't mean Labour has to "abandon its core principles". Labour's core principles were making sure that people got access to healthcare, support, and education regardless of the situation. At the point you're going "we're sitting out this election because ideological purity", you are directly reducing the chance that healthcare, support, and education are taken away from those who need it most. You want to talk about food banks? How many people more do you think will be in food banks after another five years of Conservative policies?
Corbyn would be an excellent PM, but he wouldn't be an excellent election-winner. One day, we can fight for someone like Corbyn - when we have a candidate who is young, attractive, fresh; when a previous more moderate Labour government has managed to institute the media reforms that this country desperately needs, when all the baby boomers are dead and the current generation of people who've been fucked over by Conservative policies are the main generation. That day isn't today. Today is the day where we have an admittedly slim chance to wrestle control from a country that is, by nature, Conservative. I'm not letting that chance go.
It's also worth pointing out that Burnham is on the left of the party. Corbyn is literally the left-most figure in the entire Labour party given his voting record, so obviously Burnham doesn't quite compare to that, but you already have a very viable option to take the Labour party leftwards - and this one stands a (small) chance at winning!
EDIT: And for what it's worth, the Conservatives actually *did* do the above, which is why they're winning. Cameron doesn't appeal to core Conservatives - up until he eked that narrow majority, backbenchers hated his guts and he faced some of the most serious revolts of any PM since Major. Die-hard Conservatives think he's a wet Tory, and doesn't go far enough. He got his majority because he didn't listen to die-hard Conservatives, and made at least a sop to centre-ground issues.