Comrade Corbyn's ideas are, er, radical. They are so mad that they might just work. Spend lots and lots of money and the resultant higher economic activity may actually boost the coffers to compensate (or part compensate) for the spending. There are some respected economists who buy into that theory.
The problem is that there are also lots of economists who think that's complete bonkers i.e. there's a high chance the plan will backfire. And if it does we're even higher up sh*t creek and even farther away from anything that looks remotely like a paddle.
I think it's a case of how the method is applied more than anything else.
After all, "spending your way into growth" can take many different forms on a granular level. Two plans could share the same fundamentals but be radically different in nature.
I don't agree with Corbyn's proposed level of spending (I think the Lib Dems strike a better balance). But what I did appreciate was the fully costed aspect.
Many people thought the "fully costed" claim was that extra taxes would pay back what is borrowed. In reality though, the extra income via taxes would service the increased interest payments caused by the additional debt.
In theory, a Corbyn government would therefore take on a lot more debt, but avoid increasing the annual deficit in the process. They can then spend away, boost economic growth and shrink the deficit.
The only issue is that, as you say, the plan is very risky. It puts a lot of reliance on strong growth to balance the books. If an economic slump did happen, the country would be in a lot more trouble.
I much prefer the Lib Dems' way of doing it. Cut less than the Tories, and borrow less than Labour. Models actually showed that this would be the best outcome for the UK economy over the next decade.
Unfortunately though, most Brits appear to be allergic to centrism.
