I was going to post something which is related, but tangential to this, so I'll save that.
Like many here, I suffer from GAS. Back in the day, I had two SLRs, two FSU rangefinders, at least one Minox, and always a medium format or something quirky like a Werra. I come from an engineering background, so I love good mechanical design. And I love to 'play' with cameras even when they have no film in. I want to know the cameras very closely so I don't have to stop and think while shooting. That is more difficult with the extensive menus on digital cameras, but I suppose it can still be done, though I have to think about how to get to the effect I'm after.
It's important to get to know your machine closely in order to get better results. That said, I had a partner who was an artist, and barely had an idea how her camera worked, but got fabulous results. She just had a brilliant eye.
For someone starting out, it's a good idea to stick to one camera so there are fewer variables to allow for in getting to understand the medium. But then I think it's important to try lots of different cameras to see what suits you, so having a variety in the bag (they're no use on the shelf) is a good idea, as you can portray the same scene in different ways.
Having said that, there's a value in slimming down and focusing again, once you know what suits. I think I could ne happy if I had to just use my 35SP forever on. It'd be a shame, but it pushes my buttons for aesthetics, rf, size, lens speed and focal length etc. It can't do macro, which I'd miss. And, of course, there's no telephoto, which is a shame, but not the end of the world. I have an SLR for both of those conditions, and that stays in its bag a lot of the time. If that were my only camera, the bulk (and it's only an OM, so relatively small), I think I'd be going out without a film camera sometimes, which would never do. After all, the best camera for any scene is the one you've got in your hand. The one at home in a drawer's going to do no good at all
I wish I had the discipline to use just one camera, but I don't. To be fair, that's not just my choosing, since, with a new baby, I feel a (joyful) obligation to do the documenting, though I've never been great at family photos, nor people generally. But maybe I can take one camera for a month at a time and see how i get on. After all, the $40 challenge cameras (see? I can't even stick to one for that!) are getting a lot of clicks right now.
One camera, one lens? Sure, if that's what suits you. It leads to a close knowledge of your kit and an understanding of the limits and how you can push those in creative ways. I admire anyone who produces more than snapshots with just one body. But it's not quite for me. Not just yet.