> compression makes all parts of the music almost equally loud
What you are referring to is only one particular use-case for which a "compressor" is used during music production: Most often people apply dedicated plugins to the "master" mix (the final result to be put onto CD or sold as a file). These plugins will apply what's called a "multiband compressor" which can reduce dynamics individually on different parts of the frequency range, and often do quite a lot more magic than what I claim to understand. -- Done excessively the result is the mentioned "always one volume" result of the loudness wars.
The compressor as a tool isn't limited to this use-case, though. You will, for example, put it on individual instruments' track to shape the relative strength of the percussive and decaying content of an instrument, a drum or a plucked guitar for example: Typical compressor plugins have a attack-time which shape how fast the reduction of gain follows an input signal. If you have this slower than the duration of the percussive sound, the instrument will sound more "agressive", instead of being leveled down, as the "attack" sound is increased, relative to the resonating portion. -- The end result sounds just like the exact opposite of the excessive master compression people complain about.
Then you will invariably have unintended peaks in a real-world recordings, and if you don't want to level down the whole recording to account for those peaks, or manually level them down for every instance, you'll also employ a compressor plugin on problematic tracks.
Then there's the possibility to filter the part of the spectrum that will trigger the compressor (it's "sidechain") or to let a compressor be triggered by one instrument (or group of instruments) and act on the signal of another instrument (or vocals, or group of tracks): That way you increase the percieved separation of different voices in your mix, again increasing the perceived dynamics of a song.
So, if you really want to find music with no compression at all, you'll likely only find classical recordings made only with one single X/Y microphone pair... :-)