Not the original topic, but I would agree that lesson horses in the US are a dying breed. When I was a kid I rode at an urban barn that had around 30 lesson horses ranging from beginner to advanced. That barn no longer exists and the biggest program I’ve seen lately had about 10 horses and is pretty unique. Most programs only have 1-2 lesson horses. If you don’t own a horse and want to ride something that can go correctly and is sound enough to hold up to more intense work good luck findings something without some behind the scenes connections to a part lease type situation.
Regarding the vienna reins and german martingales I think you don’t see it here in the US because most beginner programs are hunter places where there is zero emphasis on a horse being together and round. That said I have seen 2 trainers recently using bungees on horses with beginner riders which if set loose I think are faily forgiving and allow for a stretch but not for the head being flung up and super inverted.