I like this. It would really throw a wrench into the works as well as force some tough decisions by coaches. For instance, who do you pull first? Do you go with a roster heavy on strikers and risk diluting your defense, or save your midfielders for mobility and one top striker up front? The amount of time would likley depend on how the teams took shape after the second or third round of removals.
Interesting. Then again, I think anything would be an improvement on shoot outs.