If there was a YC/HN supported cofounder matching program, I'm guessing it would have a lot more success than other attempts that have popped up. However, some important qualities of a good cofounder match are hard to quantify and require serious (and often confrontational) interaction.
Perhaps if YC let individuals apply without an idea to a loosely structured hackathon/conference, some good relationships would form. YC could fund the whole thing, and take a small stake in any resulting companies. Though, that's a little bit legally murky, so some consideration would need to be put into the means by which YC would benefit.
I did apply for the YC summer batch 2016, and for the YC fellowship through "Apply HN". I wasn't selected but someone saw my application and contacted me to become my cofounder. It didn't end up working out but I can see how public applications can be a way to meet cofounders.
Perhaps if YC let individuals apply without an idea to a loosely structured hackathon/conference, some good relationships would form. YC could fund the whole thing, and take a small stake in any resulting companies. Though, that's a little bit legally murky, so some consideration would need to be put into the means by which YC would benefit.