A couple things worth noting, at least IMO -
1) It is not the copying of or listening to the music that the RIAA (for which entity I hold no special regard) goes after, it is the unlicensed distribution of that music.
2) The RIAA doesn't "break into someone's computer and search the hard drive"; using essentially the same applications used by those engaged in illegal file sharing, they discover files made available for illegal sharing. Effectively, the people getting busted have posted a "Here I am, come and get me" sign; if the files at dispute were not available for public sharing, they would not be detected.
3) mp3 sucks anyway, due to its inherent lossy compression; listening to most "ripped" music is almost akin to listening to it over the telephone. Even at the highest copy resolutions commonly available, the reduced frequency response, separation, and harmonics, along with other artifacts of digitizing, are objectionable to the discerning listener using decent equipment. Music copied from Broadcast FM, well recorded from a clean signal, blows away the sound quality of any consumer music digitizing scheme.
If the quality is so bad, why is the RIAA suing their customers over it?