Not necessarily heavy (except sometimes as an effect), but some compression almost all the time for artistic reasons, yes.
Most people would barely notice it as it's waaaay more subtle than your distorted guitar example. But it's there.
Part of the likeable sound of albums made on tape is the particular combination of old-time compressors used to make sure enough level gets to the tape, plus the way tape compresses the signal again on recording by it's nature.
- the pops and hiss of analog vinyl records, deliberately added by digital hip-hop artists
- electric guitar distortion pedals designed to mimic the sound of overheated tube amps or speaker cones torn from being blown out