It sounds similar to what we do with MG here. The state training squads are 15 or so riders and horses, and when training, you swap horses every race or every three races. When you go to competitions, you do 'bracket swaps' - The horses are divided into teams of five and each team gets a new bracket of horses every three races. It makes it a level playing field for everyone - they all get all the horses. It is mostly done because logistically transporting all the horses for a national comp just isn't possible, so loan ponies are used. You get about 30 seconds to get the feel of the horse before the race.
My opinion? It makes for really, really good riders. You learn to asses the horses strengths and weaknesses in about 30 seconds, and how to manage a strange horse under high-pressure situations, and to adapt.
We have a similar thing in SJ here as well - But only at competitions. The big national competitions draw horses for the riders.
I think it's great.
But not riding your own horse in lessons? That I don't agree with.