I have a coggins story to tell.
Years ago when the Coggins Test first came out (this was in the early 1970's) and was not widely used, my employer tested her mare. This mare was a really good black QH. The mare tested positive (and she was pregnant to My Bay Bailey).
She had her foal (Bailey Bay Sou) who was simply one of the best horses I have ever had the pleasure of handling (conformation AND training). The foal also tested Coggins Positive while she was nursing.. but 6 months after weaning she was NEGATIVE. She tested Negative the rest of her long life.
The mare, her dam, continued to test Positive. The owner of the Stallion would not breed his stud to her again after she did test positive and the mare ended up in a pasture with two other horses that were retired from hunter/jumper competition.
She lived well into her twenties with her two pasture mates. She always tested Coggins Positive.. and was not sick a day in her life. Her pasture mates tested Negative for the remainder of their lives as well. All three horses were put down and buried on that farm and all from the infirmities of Old Age. These horses were together for no less than 10 years with one being coggins positive and the other two coggins negative.
Yes. It is NOW the law to test before moving a horse and some states have stricter laws than others. Should you test a horse before buying OR shipping? Yes. Absolutely. Should you buy a Positive horse? IMO, no. TEST before BUYING. The OP should have tested this gelding before buying him (but that ship has sailed so no point in getting whipped up over it).
Should a horse be automatically put down for a positive test? Honestly? I can say I do not know.. probably yes if the horse is symptomatic or has shown the typical symptomatic cycles of the disease. Laws can require the horse be put down.
Would I expect every horse at a training facility to have coggins test on site? Yes. I would test my horse and ask politely about the others.
You do need to follow the law.. but I have yet to have anyone in this fight explain to me the scientific situation of Bailey Bay Sou's dam who tested positive, apparently did not transmit the disease and who's foal was positive while she had Mom's antibodies on board but who reverted to negative when those antibodies were cleared from her system.