That doesn't make it in any way efficient.
He's in a class that's obviously currently on electronics fundamentals. There's no design there, unless there's some really odd trend going on in the electric heater field that I'm not aware of. So, he'll be on Ohm's Law, and they'll be doing a lot of, "I give you two legs; find the third." One scat, many questions regarding it. So why are you trying to defend a method that gives you trash as an intermediate step? Why defend a method where every voltage divider calculation requires you to start from scratch? There's twelve of them in that circuit alone. (ignoring the big one)
When I say, "X doesn't make sense in a troubleshooting capacity, but I see how it would be useful in design," and you come back with, "DON'T TELL ME IT ISN'T USEFUL BECAUSE SEE I USE IT IN DESIGN ALL THE TIME HAHA PROVED YOU WRONG N00B" ... yeeeeah... do you see how that doesn't quite marry?
Anyway, if you want to know resistance, just put a known voltage across it and read the current.
/sigh. The method is not anything different than using adding resistances in series or using the resistances in parallel equation. Both of those are algebraically the same if you do it the slow way and start rederiving the current down each leg of parallel resistors to find the equivalent resistance. The voltage divider equation is the same class of equations. Very fundamental stuff and very efficient to use.
I have a hunch that since you haven't seen the voltage divider equation you haven't developed the intuition on when to use it.
I don't see a need for generating 12 voltage divider equations in the OP.
While I'm 99% design, I would say the small time that I spend troubleshooting some poor undergraduate lab experiment, the voltage divider can easily show how an amplifier was losing its gain by the voltage division of the series resistance of a voltage source to the base biasing resistors (yeah we were using BJTs as the time).
Do you find an actual voltage reading to be a magical entity completely disassociated from paper calculations?
If you figured out it was a biasing error from a voltage divider calculation, the same number taken off a direct reading shouldn't be giving you this much difficulty.