The input lag would be quite horrible. You'd also be at the mercy of the Internet. Let's see how much we can clusterup this mess.
I am at home (Texas), sending an input to a server in Chicago (not sure if that is where they are), which is a path losing packets like no tomorrow, which is then sending my input to a server in Texas so it can send it back to Chicago so it can send it back to me.
The first player calling me and complaining about lag, while using this service, is going to get the "Numpty of Year" award.