There's a flawed logic to the keeping it just because you can afford it, but that's been said (and said and said and said.....
Based on the OP's thinking the domestic horse should quickly become extinct.
How could I possibly have been able to breed any of my horses (back in the day) and then part with their offspring? Obviously I bred them because I could afford to, so I should then keep their offspring? I guess only people who currently own horses capable of breeding will be able to own a horse? (So likely his wife wouldn't have a horse then). Selling a 6 month old was always heartbreaking, but that's why there were bred.
Selling a horse you no longer need is how other people (possibly like his wife) usually manage to get a horse.
The very first horse I ever owned (mine, a gift, it belong to me not some member of my family). I trained her (with some help), worked cattle, often traveled 20-40 mile days on, hunted on and slept about 50 feet from her pasture. The day came when I would no longer be able to make use of her and she wasn't being used by anyone else. I had no shortage of people who wanted her (just being able to shoot off of her put her in demand). I gave her away to a guy I'd gone to high school with who had a couple of good homes that wanted her (working horses were always in demand). I didn't sell her because I couldn't bring myself to, but I gave her away so she could continue to be cared for daily and being used and appreciated for her abilities. I'd have felt far worse leaving her on the farm to be unused and as a result under appreciated. There were no "ornamental" animals on our farm.
I shudder to think what the OP would think if his wife was spending time on a working farm with cattle, hogs, goats, etc....that were being turned into steaks, hams, etc... at certain times of the year. How horrible that would be....we're eating our pets. We obviously could afford to have them and yet we kill and eat them? Yes, we do (even the calves I "bottle" fed from 3 days old). There's a "pang" of pain, but the steak tasted great
Oh, and people get rid of dogs too. Otherwise the ASPCA would have their work load cut in half (and don't dare take into account the number of feral cats that result from being abandon).