I do understand the practical effects. As a general matter, a team that has a lot of money and wants to win using mutants will do so under any set of rules that allows them to do so. The problem is finding a way of making it unpleasant enough to do so in as uncomplicated manner as possible
Problem is, that this idea makes last minute mutants purchase even more attractive than now.
It doesn't matter whether it's complicated or not, problem is that it works in opposite way than expected. So it isn't improvement.
I made successful "mutants trick" once in past and with Your idea it would be more profitable than now.