It's probably worth remembering that the last time YC talked about the number of applicants (a couple of years ago), it was something like 800. They usually accept about 20, and given the way the model works it's probably not possible to handle more. Now, of course half of those are probably applying on a whim--just finished college, or whatever, figured "Hey, what the heck, let's try getting rich...or at least continuing the college lifestyle for a little longer."--but even if we can assume that 50% of applications are complete non-starters, that's an awful lot of potentially great companies that get the "no" from YC.

The tech industry lived without YC for decades. You can definitely start a company without YC approval, and it can be successful.