If I Owned Prose. . .
There are some excellent suggestions presented here, so far, a few of which I believe should be addressed:
1. A profile page with the ability to customize the theme and the ability to share more about ourselves and/or what we like. A field wherein a writer can express what styles of writing they are interested in, what style they use the most, and what draws them to writing in the first place, as well as the motivation behind writing some of what they post.
2. The suggestion of being able to post videos I like, but I believe I would amend it to audio at first. The ability to read aloud one's own work the way they picture it, so that others can hear it how it sounds in one's own head would be a powerful tool and a great draw to new users.
3. A challenging word game, like Word Soup or some such, would be a fun way to draw more people to the site, and would encourage users to not only spend more time on the site, but to write more, as well.
I do have an idea that I don't think has been mentioned here, however:
In the vein of Coursera and its ilk, this site could offer online classes in writing verse, fiction (plot, character development, etc), and nonfiction. This would not only be profitable for the site (it would help to cover server costs and future challenge payouts), but it would also help to better the abilities of writers the world over, which, in my opinion, is a cause worth pursuing. The more you help writers to improve their craft, the more chances you have of not only increasing the amount of published authors out there, but you increase the chances of someone becoming a famous writer and attributing their rise to fame to this site, thus drawing more would-be writers in.
Webinars are a great way to present online content with the feel of a live class at a fraction of the cost, and keeps the students feeling that the information they are being taught is "fresh," as opposed to "canned courses" (I just made that phrase up).
In addition to online classes, TheProse could host a live weeks-long seminar or masterclass on writing (believe me, there aren't enough, and most of them are exorbitantly priced). The reasons I stated before for the online classes hold true for live classes as well.