What is the benefit of using carrier frequency for an amplifier?
Back in the day when op-amps and instrumentation amplifiers didn't have amazing DC input offset voltage levels and temperature stability, AC excitation of strain gauge bridges were used in conjunction with high-gain AC amplifiers.

Using a high gain AC amp meant you just AC coupled the amp to the bridge and forgot all about DC drift problems.

This solved the problem of dc drift but these days a typical op-amp can be bought that is superior by a mile compared to the middle years of the last century and AC amplifiers are nowhere near as commonplace.