If it is a truly random player then it would have to be very very cheapr indeed.
Its ok for people who already own an iPod of some description (or another HDD Music Player). Sometimes I like the idea of only have random music. However for people who do not own an iPod why would they buy this machine if this is their first Mp3/Music player? I want a flash machine with a screen because even if only
sometimes I want to see what I am listening to its still better to have a screen than not (even a crap one). Why buy a machine that limits you? I might buy one if it was very very cheap beacause I have an iPod to fall back on all those times I want more control over what I listen to - but most people don't have this.
It would have to be cheap, have a very long battery life (30 Hrs +), look great, and have all of these random ideas as optional (which they will be I hope, and if they are where's the USP? and if they aren't who wants that lack of control?). If it had a built in radio that would be tempting.
Alternatively - make it a DAB radio and be done with it!
In fact that would be a good idea if only Apple could improve the power consumption of DAB chips and make them smaller! - which they won't as DAB isn't really used (at all?) in the US.
I would definately buy a personal digital radio by Apple