I suspect some people will feel uncomfortable uploading their nicely crafted assets to your server. They’ll be worried that their assets may appear on turbosquid.com a few weeks later. Cynical buggers!!.
Also, there are other more established free services around that offer much more storage space. Although they don’t have ‘Unity’ in their name, so hey, that’s one advantage you have!.
Perhaps to help make it more relevant to Unity you could try to adapt it so that it will automatically synchronize projects between friends. Although I’m afraid that still doesn’t solve the trust issue.
In that case have you seen https://www.dropbox.com/ or any other similar service which offer multiple gigabytes of free storage and exceptional tools for sharing files?
Of course, there is no way around that on any site (including popular file shares)! But, for the cautious, if you own your own server, you can use hosting on that. And then UnityConnect can be used as a mode of transfer. Of course, I’m working on buying a new server with more space. But for now, It would be better to use your own server.