This is a very common suggestion in any game that includes drafting or deckbuilding. I have played a few events like this in Magic: The Gathering and other games - I feel confident saying these sound a lot more fun than they are. Playing a non-function deck full of terrible cards isn't very fun at all, especially not for prizes. The worst feeling is when your opponent just happens to have a good combo despite your best efforts to build a terrible deck and then they beat you with it.
Think of all the posts where people complain about Draft being unfair because they got a bad draft - now imagine we TRIED to make that happen every game. It's a recipe for disaster and I promise we will never force this mode on our player base :)