This is a very important point. It's remarkable how often startups run out of money as if by accident. The fundamental reason is that although a startup is nimble in many respects, financially it's like driving something very big and heavy. You have to be "ahead of the aircraft" to a degree most people have never experienced. Plus when startups are doing badly, their founders are usually in denial about it. And denial in a situation where you have to think far ahead is a terrible combination.
As part of YC business dashboards, are financials ever included? I don't mean Stripe/Braintree/etc transactions (although that's important as well), but burn rate/time remaining data. As you point out, its a critical metric and should be at the front of everyone's mind.
How carefully the startups watch this sort of thing varies a lot, but it's always the beginning of any conversation I have when I check in with them.