The problem is... which first principles? Say your goal is to get to the moon, and the principle you use is to minimize the distance, and you choose to do this in a greedy fashion. This will have you climbing ladders, trees, buildings, and mountains, and you will record that as progress justifying the approach. But you haven't reasoned far back enough to figure out just greedily minimizing your distance to the moon is never going to get you there, no matter what. Choosing the wrong principles can lead to local extremes which can be a lot harder to see in cases less obvious than going to the moon.
Reasoning backwards has its own traps as well.
Based on the moon example, it seems you define it as a set of principles you can base your decisions on? E.g. to get somewhere, you must minimize your distance. What makes something a first principle?
I'm asking because my understanding is that "reasoning from first principles" is just taking a step back, asking yourself what's really the goal and reasoning backwards. But it seems like you've got two different concepts (first principles and higher order thinking), which makes me think you've got it figured out more than I do.
First principles are not an ideology; they are more like laws of nature. Due to that, they are great both for reformulating a problem, and checking solutions.
That's the ideology.