I had an ultimate fallback for high school physics. Start putting stuff in likely equations where the units work out to the desired answer. That always worked, save for two or three occasions. Unfortunately, once I figured that out, that let me be lazy and kept me from learning as well as I should have.
When Wolfram Alpha starts solving word problems, time to start worrying. Not about machines rebelling, but about cheating in grade school math classes.
With known equations, then yes, dimensional analysis is essentially just a form of bookkeeping that helps you verify your math as you go.
But once you get into using quantum field theory to study new systems, the standard approach is to concoct a conservation of energy equation by summing terms, where each term is a combination of the system's variables with units of energy.
From there, you can discretize the coordinates and predict the existence of various particles (or pseudo-particles, depending on what kind of system you're describing) and their dynamics.
When Wolfram Alpha starts solving word problems, time to start worrying. Not about machines rebelling, but about cheating in grade school math classes.