The horse would get registered ONE TIME - with USEF - and USEF would issue a sheet of bar coded decals with the horse's info on it. To enter a horse in a competition, you simply peel off the decal and stick it on the entry sheet. Show manager scans the decal, and voila, your horse's info goes into the database for that show, and is there to be uploaded to USEF/USDF/USHJA/USEA with the show results.
This will, of course, require cooperation among the various organizations - which will never happen in my lifetime - and will also require show managers to buy a bar code reader and use appropriate software to manage their show information - which many will grouse about - but the time and money savings down the road could be enormously beneficial for competitors, show managers, and the governing bodies.
Yeah, it's a pipedream this will ever come to fruition, but it's the season for dreaming, anyway.