The line isn't purely arbitrary, it's a reflection of the reality of what most people expect from sports: we want them to be a contest of human skill on the part of the athlete, not just the amount of money someone is willing to spend on the team. We also want underdogs to have a chance, which is very hard without some sort of limits.

You could probably accomplish something similar by strictly capping spending per team to force people to do real engineering and optimize their play accordingly, but the result would be a very different sport that would appeal to a very different (and probably much smaller) audience. Formula One and Robot Wars come to mind.