What we've thought about the most is creating a better way for potential cofounders to meet each other.
There are more single founder successes[1] than VCs would lead you to believe. Maybe not so many in the unicorn category which is all VCs really care about - but you're not a VC, it's not unicorn or broke for you. I think most of us would still consider it a success if you only managed to replace your income, but got to work on something you enjoy and to be your own boss. But you'll need to bootstrap rather than secure VC funding if your company doesn't have unicorn potential.
That said, being a single founder is HARD. You need someone else to talk to, to bounce ideas off, to offer emotional support during the dark days where you doubt yourself and can't see a path to success. But you can get those things from other people, you don't have to have a cofounder.
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.
There seem to be similar challenges to creating a scalable solution for finding an SO/spouse (another unsolved problem).
For example a mountaineering class at the National Outdoor Leadership School puts students who don't know each other, and might not know anything about climbing, into serious high-mountain situations for a month. At the end of the class, groups of students head off on "small group expeditions" for a few days without instructors. NOLS has an excellent safety record and students often form strong friendships.
The military is another institution that takes people who don't know each other and quickly forms bonds of trust and mutual understanding to perform under very serious conditions.
Granted--those are carefully managed situations where the people are facing shared challenges. But maybe that's what YC would need to create in order to foster an environment in which founders can build strong enough relationships to feel comfortable building companies together.
Like you said, in a constrained environment like the military, it might be possible to achieve this in a short period of time through deliberate actions. I'm not sure how much that approach would prepare potential cofounders, since they're going to be operating in a much more ambiguous and freeform environment.
I think YC would agree that people in the same YC class make some outstandingly strong friendships.