As a former sound engineer, I agree with everything here. Just one correction 'sound check' doesn't add compression to a song but rather adjust (down) the volume of songs that are perceived to be louder. This is referred to as "normalization". Note: it does not adjust (up) the songs that are perceived quieter if they have peaks that are 100%... because they would clip. To get them louder would require a process of limiting and compression.
