To Purchase or Pass

Nope. Your daughter deserves a horse than can teach her how to do this. Even with this amount of years of lessons, I am surprised that her trainer is recommending such a green horse. She should have had experience learning to train WITH a trainer first, FOR YEARS, and then buy.
I bought my first herd of middle aged, been ridden and been there, done that horses. It was a wise move.
This purchase is going to be learning lessons the hard way.
I have read and watched videos and programs about international riders. Many of them learned to train, then did catch riding before they EVER bought their first horse, and most of those first horses were about 12yo and had been shown for several years. WB's are often slow to respond...and then, after being pushed Will explode bucking. That's about 2,000 pounds of bucking energy, unlike rodeo broncs who weigh much less.
Just some fyi.
Pass.

His bloodlines are impeccable, so I think he will likely not let the horse go for less than 5k. Sorry, I should have given a bit more insight about my daughters riding experience. She does have experience training horses, usually alongside her trainer, though she also trained an adopted mustang by herself for somebody she knew that later used the horse as a guest horse (she has experience western and english). We would be having our trainer get up on the horse at least once or twice a week for the first two months or so.
My family had been breeding, training and selling Hanoverians until two years ago, and the horse we bred for my daughter had colic and did not survive the surgery.

I appreciate all the input and areas I had not considered about this horse. I suppose we will be back on the hunt.

Absolutely pass.

For $20,000 you could buy a cheap horse that just needs training, without soundness issues.

My friend and I were just discussing the differences between a $500 horse and $10,000 horse. She takes in cheapo horses all the time, trains them and sells. Mostly as a hobby.

I had another friend buy a $10,000 horse who she was terrified of as he reared near traffic. That friend would have been better off spending $1000 or $2000 and getting something dead broke and calm.

I would focus on a horse with a passing vet check and spend the extra money on a full set of x rays, and drug testing. I would rather get something young that has only been lightly started, and is not being jumped too young.

I remember seeing a seven year old holsteiner who was already crippled and being sold as a broodmare only. She was jumped cross country and messed up from being jumped too hard too young.

If you are looking for a warmblood I would probably purchase a younger animal like 1-3yr old, and invest in training. There are several issues with buying older horses, as they could be injected with adequan or other arthritis drugs and you would not know until the horse goes lame months later. Even young horses are sometimes injected in their joints.

Finding a sound and sane horse is not always easy! Make sure to invest in a full set of x rays and flexion testing! The racehorse trainers often have the heart checked as well.

I would personally look for a horse out of a stallion who was shown even into his teens. A horse that is retired early may have had early onset arthritis. Arthritis is partially genetic and you want to avoid a horse who is not going to stay sound. Definitely try to see the side and dam or the horse you are buying, if you can. If they are sound, that is a good sign.

Proper conformation is important too, but I've seen horses with horrible conformation stay sound, yet the nice looking animal is crippled. Definitely a genetic component to joint health.

I was thinking this horse could be a good match for your daughter, despite all the problems (assuming vet check is clear, including a blood test for sedatives!), up until you stated the price.

There is no way a project horse- and that's what this is- is worth $20k, no matter how good the bloodlines. Geldings are an end product- that is, the bloodlines mean squat except for how they manifest in this particular horse because a gelding is not a breeding prospect. If he has very good conformation, I'd think $3-5k would be reasonable. Any moderate conformation flaws would drop the price a bit, and larger conformation flaws (still not affecting soundness) would put him at $1.5k max in my opinion.

This horse has been poorly trained, which is worse than not trained at all in many cases. He's also underweight; many people find that the sweet, skinny horse they brought home has a major personality change (and not for the better) once up to healthy weight again. It sounds like your trainer is on board with thinking your daughter can handle these issues and can work with her to make sure things are done right, so I will assume that's not a deal breaker (though it does, of course, affect the value of the horse!)

The question is if you want to deal with the dishonest sellers- you have to pretty much disregard everything they say/claim that's not provable. That means getting a very thorough pre-purchase exam, making sure all registration paperwork is in line, etc.