I have some questions about step 1 (find a flexible program):

My understanding is that there are two sources of inflexibility for PhD programs: A. Requirements for your funding source (e.g. TA-ing) and B. Vague requirements of the program (e.g. publish X papers). I'm excluding Quals, since you just have to pass a test and then you're done.

Elsewhere in the comments, someone wrote:

"Grad school is free. At most good PhD programs in the US, if you get in then they will offer you funding which covers tuition and pays you a stipend on the order of $25K per year. In return, you may have to do some work as a TA or in a professor's lab."

So, there are two types of jobs you can have to fund your PhD (TA-ing and being a RA/Research Assistant to a professor). How time-consuming is TA-ing generally? I imagine it varies based on the school/class. How do you find a TA-ing gig that isn't time consuming? Can you generally TA during your entire PhD? I think I vaguely recall a university that only would let you TA for so many semesters.

You could also fund your PhD by getting a fellowship. Philip Guo has written about applying for the NSF, NDSEG, Hertz fellowships. I'm poorly calibrated about how hard it is to get one of these fellowships. I've also heard that certain schools will offer fellowships to some of their students. How hard are these to get relative to the fellowships mentioned above? There are ~33K science PhDs awarded each year. I wonder what distinguishes the ~4% who get fellowships from the median science PhD student.

Let's say that you were really frugal and/or financially independent already. My impression is that many schools would still require you to TA in order to have your tuition waved.

Let’s assume you have the financial aspect of your PhD taken care of (e.g. You have an easy/enjoyable TA job). What other requirements are there other than passing Quals? Could I read interesting books indefinitely until I find something interesting to publish?

I'd like to believe that achieving step 1 is possible, but as eli_sennesh pointed out, this is hard.