As others have said, it’s not about being pushy; it’s about being willing (and able) to spend hundreds a month on training and petrol to get them everywhere they need to be, it’s about being willing to sacrifice your own time and couple time and family time, it’s about being their biggest supporter and their soft landing place when things don’t go well.
What DH and I have actually noticed is that the kids of the genuinely pushy parents don’t go far. The parents push and push and the kids might get through say the swimming levels very quickly but any love for swimming gets lost along the way. We’ve got two kids who compete at a high level for their sport and pushy parents at these levels are rare, but I’ve seen loads of them in the lower levels of the sports as the kids have worked their up.