I've met a few retired showjumpers and dressage horses over the years. A very common thing is once the horse starts to get a little old for the top level competing it goes out on loan to a young rider as a "schoolmaster", then when they get a bit older they end up turned out in a field for most of the time, well fed and brought in during bad weather, getting vet treatment, their feet trimmed when necessary etc - basically kept as well loved (expensive to keep) pets.
I've had lessons riding an ex-international dressage pony that my teacher had taken to international level when she was in that age group, he was about 22 (pretty old for any horse or pony) and if he didn't get wheeled out & ridden now & again he would fret.
We also had a horse who was a family all rounder, who I show jumped at local level. When she got arthritis and was retired, I would occasionally hack her over to a local show 10 minutes ride away where she would get all excited & start dancing about every time we went near a ring. It could be hard to persuade her to go home.
But then many people kill their family member dogs when they get old.
When they get old, infirm and their quality of life isn't good. I had to pts an 8 year old cat because he was dying of CKD, broke my heart doing it but he was miserable & confused and had very little quality of life, so it was the kindest thing I could do - a few more weeks or months with him getting skinnier & skinnier, unhappy, crying out in the night, vomiting what little food I could persuade him to eat, or going to sleep peacefully in my arms surrounded by love. Animals live in the moment mostly, and keeping them alive for the sake of it is more cruel than PTS when they get to a certain stage.