It is not the funding that is the main reason for applying. Although some small amount of money is great to cover living costs so that you can devote full time to your project, it can be handled differently. What I think most of the people here are interested in is the post funding period - getting big investments and connections through those that already did the talk and walked the walk. Note that I am not referring to YC only, but also to all those that YC helped or involved. There is a lot to learn from such condensed entrepreneurial community.
However, don't idolize YC. They are not best. They are not even the first ones to do so. They are just best known and publicized.
I would highly recommend doing a criticizing and constructive thesis. That is - seeing the shortcomings of YC and suggestions on how to do it better. Your question to HN should be how to do it better?
Such thesis is benefiting to all then, YC and other that are copying the model, but most of all - us :)