Just to echo what everyone else is saying, in my area, there are fewer and fewer lesson barns, period. Most barns have one or two lesson horses (usually TBH, not very fun horses to ride) for dead beginners, or for skill assessment for people’s first few riding lessons. Then there is strong encouragement to lease a horse. My last lease at a small private barn ended, and I wasn’t able to find a new, suitable lease within my price point. I’m at one of the few lesson barns I know of (just to keep riding) with multiple lesson horses and I’d say the highest I’ve seen horses jump in any lesson is 2’9".
From the barn’s perspective, it’s not economically sound (or ethical) to have a horse that does multiple lessons a week to earn his keep to jump courses at 3’6".
I’ve heard of lesson barns in years past (like, in old horse books) having horses that jumped that height. Even assuming hazy memories and pony books are accurate, that was in an era with fewer concerns about lawsuits, less of an eye on horse welfare, and a more horsey culture than exists today in most suburbs.
It’s also worth pointing out that jumping one vertical of 3’6", one time, doesn’t mean that the horse is a 3’6" horse capable of jumping a course of that height.