Why are polarity assigned to resistors in the circuit in questions?
Assignment of polarities in typically introductory electronics questions is indeed possibly arbitrary. You want to be able to answer a question with whatever sign convention the question or schematic pose. However, when working with dependent loads/sources, the sign is important, as your work shows. Working clockwise around the circuit using the passive sign convention, I get the same result for your scanned circuit.

No, the polarities aren't there just to be confusing. They are there as a required sign convention and the results can be positive or negative, depending on the other circuit values. You just need to do the math using that convention.