It works for other social networks for a reason; Goodreads specifically is a good comparison. It seems crazy that the only place you can find a feed of what you're friends are listening to is on the desktop app, unless I'm missing something.
For me, the most interesting thing I could see on the homepage would be something like the "Recent Tracks" section on a user page, but made up of what all of your friends are listening to, including other things like, this friend attended this event, this friend commented on this song, this friend shouted her other friend... Maybe even weekly charts for all of your friends listening combined. Move some aspects of the current "Live" page to this new feed, move some of the last.fm editorial content there... it just seems like there are so many more interesting things that could be on the homepage, that would be constantly changing and interesting to check on frequently, as opposed to the recommendations. They should still be available, but 99/100 I'm not going to last.fm for recommendations, I'm going to poke around at the fun data and see what's new!
I originally posted this on Reddit, and a commenter also suggested this: "I'd also put the album releases feed there, and perhaps also events." Love it.