Wren, I do get your point but then I think, why would you want your child to master the piano if she doesn't love the piano - (or insert any other category here) - so she can go on and be forced to continue to do something in a field that she doesn't love. I think you can encourage her to master something, but it should be something she is really excited about. Mastering something without having a passion for it is akin to taking a job at a fast food restaurant, yes, it provides a pay check, but how long can you really do it when you dread doing it every day.
I see too many people doing jobs that they dislike because they didn't know what they wanted to be when they grew up or they changed their minds later on after they realized what the career path was actually all about (this even includes some doctor friends I have). Yet they can't change the course of their life (or at least they feel they can't) because they have too much invested and are living out their parents dream for their future, not their own. They had no passion for the profession that they picked, they just knew that they could master it.
I would rather let my child plan their own future, while I guide them and show them the options available. They can go to a state University or an Ivy League school (obviously, if they can get in) but wherever they go, it has to be their choice, not mine. I just want them to be passionate about what they do, so they can be happy doing what they worked so hard for.
I guess I consider my job is to make sure she has options available to her, not to paint her into a corner so she has to do what I want, instead of what her heart desires.