[paulat]

You would probably wind up with a spectacular horse, but it would not be eligible for racing nor would any of it's offspring.

Why is that (I am asking the question honestly). What is the difference between that and putting him out to stud?

Is there a rule that it has to happen "naturally?"

[wagglebee]

Yep, that's the rule and there is no way around it.

[Help!]

The Jockey Club that registers Thoroughbreds mandates that all matings be by "live cover."

You could use the semen on a mare of a different breed, such as Quarter Horses, Warmbloods, etc. You could race the QH in Quarter races. Or you could use the offspring for another purpose such as jumping or dressage, or barrel racing, etc.

But you could not get a registed Thoroughbred. So any offspring could not be used for Thoroughbred racing or breeding purposes.