Why does Linux use non-free codecs and why are codecs needed at all?

Say a song is recorded somewhere on the planet with a computer, and that stream of data is stored. If this is stored using Audacity , you can set it to .aup format, which is a very simple XML file. Why do we need anything else than a few data points in a file? Why would we use .mp3 or anything? In fact, encoding this increases the size for a few local samples. I think the issue could be size for images for example, but I can't say that for audio files.