It would seem apparent you dont live in real music territory, up here 90% of music files are mp3's for a reason - they go further than anything else and are more reliable. When you listen to music in the remote corners of Arnhem Land then these things become important to your very survival.
(Ahem.)
To have perfect quality, there must be no compression. For a small size, there must be compression. You lose the sound quality over time with this constant compress/uncompress process.
Not quite. You can compress without loss, like some formats do already.
What you are talking about is lossy vs lossless compression. All your favourite file compression formats (RAR, ZIP) are lossless because if you lose any information, your warez - sorry, backups - get sad.
The obvious reason that lossy formats (jpeg, mpeg, H.264) compress so much more than lossless (png, FLAC) is that they can throw information away - the big difference between different formats is how they decide what to throw away. This uses a lot of theory about how we perceive things, like can we tell tiny differences in colour apart, or tiny differences in sound.
A little bit of loss in the music information really isn't noticeable, unless you are a deluded audiophile with $30,000 digital cables and a $10,000 pearwood volume knob for better music colour. (I'm not talking about the difference between 128kbs and 256kbs, that is noticeable, unless you only listen on crappy headphones or bad car radios.)
Btw, there is a way to compress some music really really well, absolutely perfectly - it is called sheet music. Except you lose the information about how it was played.