Very well said! It is true that once you grok this technique, you are basically unstoppable. It does make for slow progress at first, but it's worth it.
Edit: I went to grad school for math, and I got there by pretty much doing what you described!
Edit: I went to grad school for math, and I got there by pretty much doing what you described!
I recommend the Art of Problem Solving community as a great place to start. I have no affiliation with them, they're just awesome for math learners of all levels.
a) fast at the beginning, then gradually slow down, e.g. rote memorization;
b) slow at the beginning, then gradually speed up, e.g. deep understanding;
c) slow at the beginning, then remain slow forever, e.g. doing something chaotic and stupid.
The problem is that sometimes you have incompetent people who use the third kind of method. Then, when things blow up, people start paying close attention to the speed, and reject any method that is slow at the beginning, because they suspect it would be the same story.
(In other words: premature optimization, technical debt.)