That is much less common, but simply having two flights with the same number in the air at the same time is normal. I was surprised at the comment that ATC had issues with it.

UA should have cancelled the original flight and operated a replacement segment as you suggest. I can't think of any reason not to do so besides artificially inflating the completion rate at the cost of depressing the average arrival statistics. The DOT should probably put in some kind of cutoff -- any flight more than XX hours late is considered to be cancelled. That would eliminate the motivation for these shenanigans. If I were a passenger on a flight that was delayed until the next day, I'd consider it to be cancelled personally.