I presume it works in American sports because it has been the model from the beginning? I like that there is no relegation/promotion in those sports because it makes sense in the American context, but it has no business in European sports.
A max wage budget and especially max season transfer spend could easily be implemented right now and not at all affect the rest of the game as a whole. Don't you agree? Lets say that teams can only spend 100m a season. Thats doable isn't it, if you care about fairness? Some teams could afford the whole 100m, others couldn't but it creates a more level playing field.