but also be able to browse by artist (without doing a search.)

I browse by artist all the time. Just make Artist playlists. An example of doing this is shown here.

You can, if you like, have the artist playlists be in two places: Both beneath the Genre playlists as well as all grouped under a "by artist" playlist. And if you do it correctly, they'll be the same playlists. You don't have to create two sets of artist playlists, just copy them: when you copy a playlist, it's just another link to the same playlist. Details here.