Sounds simple in a competitive setting. The organizers would just need to line people up into 2 rows with the two players on opposite sites if you’re playing melee or something, separate the two players by a table and put the monitor on the table. If the TO has a lot of monitors or is just balling like hell they could just have two monitors per game, though I don’t know how the cables and lag and such would work.
Of course, in casual play the solution is very simple: stop playing with the bum. 
Is it cheating? I’d think the concept of what is a factor of skill would end at the same point as one’s hands. There’s always going to be the mental aspect and shouting and all that, but I’d say that the goal is to just have it be two good players going at it, but that’s just me. Personally, I like that Lan parties and online play eliminates the screen watching issue myself.