I would be interested if you have some pointers. I've tried searching a bit but didn't hit anything.
Intuitively there is a lot of things that I want intrinsically to do, but I will do a calculation wether I'll have external motivations/rewards to do it and decide from there.
For instance I intrincically like programming. It still doesn't mean my intrinsic motivation to program disappeared because I get paid, nor that I won't be exploring thing that I am curious about and try to align external motivation to help me explore them.
> if you start charging parents (punishment) for coming late to pick up their kids from daycare, parents will become more late.
I know this case study, but as a parent I don't see this on a personal level. To put it on a different case, you get fined for parking on priority/handicaped places, but don't see rich people everywhere abusing priority parking. Some do, but most don't, so at least a majority of them don't see it as just an economic transaction. As usual, reality is more complicated.
As soon as adults feel extrinsically motivated, they start to view the situation as an economic transaction, where they will only perform tricks for treats. Typical real-world example of this: if you start charging parents (punishment) for coming late to pick up their kids from daycare, parents will become more late. One can speculate that this might be because they start thinking of it as "paying for extra time" rather than "being a nice human being to the daycare staff."
The cases you mention where they do indeed apparently coexist, I suspect (but have no data to support) that the children successfully manage to ignore the extrinsic motivation because the intrinsic drive is so powerful in that instance. It's probably not a sustainable model to rely on that happening, though.
Drive is decidedly not a self-help book. It's a summary of the available evidence in support of and against the existence of intrinsic motivation and how it relates to the other types of motivation (extrinsic and physical and emotional needs.)