Why use bridge vs. other measurement circuits for thermistors?

Yes, that's how you will need to balance your bridge (Zeroing) for the temp you want to establish as reference.

What is important, the resistors/impedance used in the legs of the wheatstone bridge could be of different RANGE - ie. in one leg ~100ohm, in the other 100kohm, end you will get the same results.
And, we talk impedance, so in one leg you may have resistors (or a potentiometer) and in the other resistor and capacitor/inductor, again even with quite different range, and with AC excite voltage you get again the same results.
So with a single value of the potentiometer in the first leg you may compensate to zero the thermistor of ANY value in the second. Used for precise measurements for maybe 200 years already..