Question regarding how to slow down and enjoy academic life
It may not be necessary to wait until you've reached the end stages of your career to have time to explore your research. 

If you are able to get fellowships to fund your graduate career—or to find a suitably understanding advisor—then it may be possible to "slow down" your graduate career. In such a case, you'd be able to handle things at your own pace (within reason). That's how I managed to take my time doing my Ph.D., and it allowed me to work on problems I was interested in, rather than other problems.

Similar funding does exist at the professional level, such as "named" fellowships at the US Department of Energy (DOE) laboratories, and through grants like the MacArthur Fellowship (also known as the "genius grant"). It is certainly not easy and straightforward to do, but it could be a way to get the freedom to work without additional responsibilities.

Outside of academia, I don't think the situation improves much. For instance, at the DOE laboratories, you're only able to pursue your own research if you're able to secure your own funding to do so (or have moved so far up the chain that you are a laboratory "fellow," and can do what you want). Similarly, in industrial research institutes, I suspect similar issues apply (you might not have to worry about writing grants the same way you do in academia, but you'll still be expected to "justify your existence" on a fairly regular basis.