Imagine, for a thought experiment, that you were running YC and Mark Zuckerberg came and said "I am done with Facebook. I want to do YC but I don't have an idea right now."
You would feel pretty stupid turning him down right? It's a reasonable bet that whatever he did next would also be successful. At the very least you'd be scared to bet strongly against him.
There are many people who, while not being so famous, have accomplishments and abilities of some kind which could inspire a similar feeling.
I'm surprised you're willing to consider single founders at all. No team, no idea/product... what's left?
(Disclaimer: I've applied many times as a single founder and have gotten justifiably rejected.)