Yes, sometimes it happens, but it doesn't usually take too much ingenuity to avoid getting into this awful situation.
Because the airlines policy was to overbook. It appears here that the seats were needed for operational reasons. If you don't get enough volunteers you have to remove people who don't want to be removed. There are varying degrees of that, and in the worst case it might be necessary to deplane everybody and start again. Far better (and likely quicker in the circumstances) than ending up in this mess.
Again, I don't understand, you just keep raising the price until you get volunteers. It doesn't take more than 30 seconds. Ring your call button if I have any takers at $2000, $3000, etc.?
The only reason I can think of is United it too tight to do that.