For anyone curious about Japanese Thoroughbreds, they are actively trying to breed really good white TBs there. This is the filly currently racing;
https://www.nytimes.com/2022/05/16/sports/horse-racing/rare-white-thoroughbred.html
And to see how fantastic a minimally expressed dominant white spotting gene can look, scroll down the page and take a peek at
her mother. There's a link in the article to another article about her, but here it is as well.
https://www.horsetalk.co.nz/2016/01/08/new-spotted-wonder-white-thoroughbred-wins-japan/
I have a good friend that works with TBs and she and my daughter are plotting to save enough to import semen from one of the Japanese-bred white TBs, since that seems to be the only place that really wants to get the color into the best racing lines.
In the US, Megson Farms snaps up most dominant white TBs.