It would depend on the findings. We don’t have a diagnosis for what is wrong with the horse. It could be a muscle disease, EPM, Lyme disease, or any number of things. Some of those diseases can have a significant impact on the horse’s behavior, yet are treatable diseases. I think the owner is probably wise to turn the horse out with time off and see if anything shows up later down the road.
Alternatively a $1-2k vet workup to see if they find something is reasonable just so you don’t have to second guess that you may be euthanizing a healthy animal.
Donating the horse works too. Some universities need treadmill horses that just need to be capable of running on a treadmill and safe enough to handle on the ground. He might be perfectly fine for that.
I would probably want some x rays of his spine, and teeth as both can cause issues with explosive behavior under saddle and at least a basic neurological exam before I totally gave up on him. And maybe check vitamin E levels in case he came back deficit. It’s at least worth looking into.
I’m not suggesting she spend a ton of money on him, but I would at least attempt to get a vet exam and see if they have any ideas before taking his life.