As a lifelong type B'er myself, I have to admit that I have a hard time understanding this thread and the expectation that a young person always should have intrinsic motivation, or be goals-driven. Sometimes that's just not who they are. I admittedly struggle to give things 100% all (most) of the time - I am the classic jack-of-all-trades-master-of none. I ran varsity track and was decent but could have been better. Part of it was not really caring too much if people beat me, only that I was showing up and doing what I could. Part of it is also a type of perfectionism like someone else said - if you don't try, you can't fail. My parents never cared and left it 100% up to me and had they pushed, I think it would have made me feel angry and defensive, and backfired even more. I think the best thing they could have done is may help me understand why I am the way I am, and that it was OK to be who I am, that everyone is different. Granted they weren't investing a ton of money and time (and as a single parent of a gymnast I fully understand that massive investment), but there is really not much they could have done to change the fact that I simply move at my own pace.
I have very often suffered inside knowing that I am like this, because our society seems to flat out DESPISE this approach to life. At 36, I finally have come to terms with it and am actually happy with who I am. I would have struggled a lot less mentally as a young person if I had realized then that being just OK with where I was at any given point (even if I knew could be better) was a perfectly fine way to be. I may not have won any championships, I may not be driven to climb the corporate ladder, and I probably won't write that book I wanted to write. But I am a very sensitive person and friends/family have said that I have a calm way of being and listening, and I have patience and truly enjoy doing things at my own pace. I am really good at savoring the road I'm on when, other people speed down it and miss the scenery. I've watched my type-A over achiever father finally realize that his constant stress level is causing him health problems and can't be sustained, and I understand that this lightening-speed, competition driven world we live in can mentally crush people along the way.
My 13 year old gymmie, who competed L9/10 this year (her 5th year of gym) is a constant source of awe for me because she is SO dedicated and So diligent. I think she is amazing, and sure, I even want to be like her sometimes. I've even asked her how she does it! But I would never want her to be like me, not because I am bad, but because she is who she is. My other DD gets obsessed with lots of things for a short period of time and then moves on. There is no changing her. My point is honestly NOT that type-Aers are wrong at all, just that not everyone is like that. Each way of being has it's benefits and challenges.
Maybe your DD will get "only" what she gets from the sport. She may just be having fun and learning life lessons along the way. She may be enjoying the social benefits of it. She may let herself down, or maybe her coaches or maybe you, and she may even learn from that. But she may also look back on her time in gym as a bright spot that was crucial to her learning it is ok to be a person that plods through life "half-arsed" when other people are screeching by.