I think I've said it before but I'm the tough love kind of person. My parents if it were them would make me look after the horse whether I loved doing it or not because the fact is I wanted the horse so it's my responsibility to look after him/her. It's not ideal but it kicked my butt into shape! I didn't get a horse until I was 18 but my parents were right they are a lot of work.
It's not the nicest thing but 2-3 days a week still is a fair amount. I exercise my TB 4 days a week so she still is doing a fair amount with him.
Threatening to take away the horse if she doesn't commit to looking after him would work if Harley was ONLY her horse. But we share him and I ride him as often or more often that her. I spend more time at the stable than her. But that's beside the point isn't it?
I am building a very expensive barn. I bought a horse that I share with my daughter. Initially, we thought he would be hers, but right now, I'm more into it than she is. Clearly, I am not doing all this just because of her. She's barely 11. I've wanted horses again for 20 years. Finally, I get to have my horses.
So I'm not in a position where I can threaten to sell Harley because she's not looking after him (not that you suggested this). I look after him and plan on continuing to do so. She can choose to get involved or not - but if not, I'm happy to ride him.
Whether my daughter continues to ride or not, we need a second horse as a companion for Harley. Otherwise, he'll be alone. It would not make any sense to get another Harley! A quiet, bombproof horse makes the most sense. That way, I can still have a horse I can ride on trails, put a friend on, let my daughter ride if she wants to. It might even be a good, calming influence on Harley. I'm certainly NOT going to keep buying expensive show jumpers in the hopes that she'll decide she likes one!
So hopefully that clarifies my thinking. I would absolutely NEVER encourage a parent to buy a horse for their child if they're not into horses themselves. That's a huge mistake. The reality is that children are fickle, get bored, move on. They are not innately responsible (there are, of course, exceptions to this rule). These will be MY horses. My daughter will have the privilege of riding them as long as she keeps up with her lessons and rider levels.