It does seem like it would be beneficial to US breeders and interested spectators to have this information more widely available. The horse show software now used by most shows hereabouts (showgroundslive) shows the national affiliation of the riders via a flag icon. At one point, whatever awards system my horse was recorded in showed US-bred horses with a USA flag, but I thing that was something that subsequently died (PHR???).
I assume that any horse of unknown breeding/birthdate isn’t going to show up as US bred (or European bred), but any horse that’s done an age-related division (young hunters or young jumpers) has to have that information in the system. I don’t know what sort of data, if any, is required for green hunters.
I watched a portion of the Oaks-Blenheim Young Jumper finals yesterday. Not a lot of US bred horses there. The highest placed US bred horse in the 6 y.o. group was third overall.