Sorry but I'm not quite sure what you are disagreeing with, Immersion.
Your basic compressor (not multiband) is for controlling amplitude without respect to frequency. So it can smooth a mix that has harsh peaks by knocking those peaks down a bit ... wherever those peaks are throughout the frequency spectrum. So yes, it can cut harsh edges or volume spikes in this way.
An EQ is frequency specific. You can also lower volume peaks with it, but always over a particular frequency range. But of course you can also use it to lower particular frequencies that are already low in a mix, which a basic compressor does not do.
What's important, for me, is not so much the individual compressors used but the individual tracks you have to master. Some tracks can be in bad need of compression because of wayward dynamics that need taming, and this is often a matter of inadequate mixing (and recording) of the track in the first place. But I'd probably still use EQ along with the compressor. Or maybe use a multiband compressor.
A good mix may need no compression, but it may still need some massaging to bring it in line with other tracks on an album ... which is what mastering is all about.
Compressors are great for controlling dynamics in a live recording environment (singer, guitar, drum mics, etc).