I lead engineering at a VC firm, and while we do sometimes help in diligence, it’s a tiny portion of our time, <1%.

Your second paragraph is spot on, and I hinted at a similar idea in a sibling to your comment. Especially at series A and later, customers are an existence proof for the product not being vaporware.

So when we are involved in diligence, it’s usually near the end, and we’re getting to know the engineering leaders to see if we can help them speedrun a few iterations by sharing best practices or introducing them to other leaders in the portfolio who have been there and done that recently.

What if they're series F and are burning €1m per month on infrastructure because it's badly designed, and haven't yet turned a profit? Maybe VCs really do have billions to slosh around... Didn't a start-up go under recently for that very reason?

We typically invest at earlier stages, so I can't say firsthand what diligence looks like at series F. If you mean Fast, Gergely Orosz had a good writeup at https://newsletter.pragmaticengineer.com/p/the-scoop-fast. Sounds like that was more attributable to hiring ahead of revenue than infrastructure spend.