Here's a hypothetical for you: how many people do you think have social permission to contact a YC partner and say "X is awesome and deserves a look." I'd ballpark that in the hundreds to low thousand range. Many of them are accessible on the Internets and less overwhelmed with suitors than the YC partners are. How about solving a meaningful problem for one of them and having the next application say "We built a $WHATEVER for $SOMEONE which increased their customer base by 10%, like they told you over email earlier."
P.S. This advice had wide application beyond YC and beyond "applications." Indeed, part of me thinks that applications (in general) are a backup filtering mechanism for people who haven't figured out a more effective way to get what they want yet.