Sometimes you have no other choice because the signal is too close to ground. This sort of "folded cascode" circuit is common in single supply opamps, the example schematic below is CMOS but similar bipolar circuits also exist.

The input pins can be at or slightly below ground, the emitters/sources are a little above ground and the collectors/drains must be lower, so there isn't enough voltage there to drive the base/gate of the next stage - the next stage needs to be common base/gate.
(I mean, OK, LM358 solves this differently by adding emitter followers in front of the differential pair and shifting its voltage up. But doing so adds offset voltage and noise.)