I find your conclusions quite strange, you have a child who is self motivated to research things, this is great, you can encourage it. Yet you then go on about lack of pushing. Pushing is pretty much the opposite of self motivated, the big thing pushing does is remove the opportunity and mental effort to pursue those self interests - you're pushed down the route that the adult wants you to go.
If you have no self motivation, then pushing might be useful - not as useful as finding a way to get that self motivation of course - but that really depends if the "coasting" is at a cost of what you could achieve longer term - ie the coasting stops you getting the grades required for your next goal.
The cost is huge, and narrows opportunities for the child, it doesn't broaden, the money spent on the school means it can't be spent elsewhere. A private school might have changed your experience of education, but so might another school, and your experience is not the same as your child's.
Your DD is happy, she's self motivated, invest in those things, not in some expensive grass is greener idea, and save that money - she might be happy in 15 years when she has the money to go spend her time volunteering on a Tudor archeological site, rather than having to get a job at the bank.