Usually in a microcontroller you have lots of analog input pins, but not many ADCs, perhaps just one. So the analog inputs are multiplexed to just one ADC.
Actually, maybe you want to have only one good quality differential amplifier. Then, you switch its input, so that it reads the different shunts (one shunt per solenoid) in sequence. This has the advantage of not needing to trim 18 amplifiers to work identically; because you're using the same amplifier for all channels, the results can be directly compared with each other more easily.