I think she'd say she does, because it's part of (for her) the experience of owning a horse. She also did that for pay as a teenager, so maybe it helps her feel young, too.
I think what you mean is that no on would miss it if horses didn't shit, and I think you're right about that.
I think we underestimate, though, the value to people of belonging and participating, socially. Many activities people don't like, on their own, become neutral or even enjoyable as part of something else, like mucking stalls.
Everything is contextual, and there's no objective, independent-of-context answer to the value or worth some thing or activity is going to have to someone.
And your mother doing something she enjoys (and involves cute animals) doesn't mean that as many people as needed are "willing" to do a crappy job for free.