reason(s) to use a 10-bit ADC instead of a 12-bit ADC?
Cost is one factor, as you note. $1 is a big difference in price for a lot of people.

Also consider the complexity in interfacing with the ADC. If it has a parallel interface, you need two extra pins for the 12-bit ADC versus the 10-bit. If it has a serial interface, then you don't need extra pins, but you need extra time to transfer two more bits1. If the serial interface is slower than the ADC, this limits the sample rate, since you can't start reading a new sample until you are done reading the previous.

This is all assuming that everything else is equal. In reality, that's probably not true. A careful reading of the datasheets is necessary to understand all the differences.

1: assuming, as The Photon points out, that the serial protocol used by the ADC doesn't transmit the measurements in octet chunks, in which case either 10 bits or 12 bits requires two octects, or 16 bits.