I think the same number of breeders would simply redistribute around the country.
For example, breeder #1 has 5 mares and a budget of $5,000 each (simplifying it). Maybe they live in an outlying state in the East. With AI, instead of the decision being based on shipping costs (limiting things to a geographical region), breeder #1 picks a stallion out of CA, TX, WA, etc. (assuming they'd be a better match than a closer stallion).
Point being, the same thing would probably happen all over the country... same number of breeders & mares, same budgets... just moving around the country more! It would open up the chance to improve pedigrees—if you're looking for a Seattle Slew son, maybe the best match is too far away... institute AI and it wouldn't matter!
In poking around looking at Warmblood stallions, the thought that I can pick any stallion I want, anywhere in the country (or even some in Europe!) is pretty exciting to think about!
Sure, there are probably a few stallions whose books would increase, but for the majority of breeders who have a stud fee limit, it opens the doors to many more choices and hopefully, the best match in that stud fee range, as opposed to the best match within shipping distance...
And, as someone mentioned, it would (I'm guessing) weed out the stallion population some...
JMO...