It's been a couple years since I've regularly used a P&S camera, but at the time I didn't use any sort of case for it. My philosophy at the time was that every hurdle between thinking about taking a picture and actually taking it meant more of a chance that I wouldn't take the picture: for me, having a case would mean I'd take fewer pictures.
When I bought my camera and it arrived all shiny and new, I knew that not having a case would mean my camera would get scuffed up -- and it did (not bad, there were no big dings or cracks or anything, but it was visibly used), but I treated them like badges of honor, proof of the adventures the camera had seen.
I did put an LCD protector (one of those clear, sticky sheets) over the LCD, though. The two really sensitive parts of the camera (provided you don't damage something like the battery or SD card door or hinge) are the lens, which of course retracts into the body and gets covered, and the LCD. So as long as you keep those two things protected, the camera should remain functional even if it gets scuffed up a bit.
I'm not sure what kind of bag you're talking about using, though. Usually I kept my camera in a pocket of its own in my shorts or pants. When I went on vacations I'd put it into a pocket in my backpack but I wouldn't put anything in there that could scratch it badly, like my keys. With a case you don't have to think about that ahead of time (as long as you don't mind the case getting scratched up), which I imagine would be nice.
(If you do get an LCD protector: I'd recommend getting one of those packs with like 6 or 10 sheets in it: the first time I put one on an LCD, it took me 2 or 3 tries to get it right (smoothing out the bubbles and cutting it to the right size and so on). Having extra sheets will let you practice a couple times if you need to, and will make it easier to replace the protector after a few months when the first one gets scratched up or starts to lift off the LCD.)
Edit: After thinking about my answer for a couple hours, I remembered two more things that you may think are important: first is that I only used my camera for one year. It was in great condition (apart from the surface blemishes) after that year, but this means that I don't know what might have happened longer-term. Second is that I lost my camera after only one year. I left it at the airport in a rental car after I returned it: because I always carried it in a pocket of my shorts, I frequently took it out of my pocket and left it in one of those cubby-holes in the door. They're really convenient for holding your camera while you're driving around, but when you drop off the car and you're in a rush to make your flight, having your camera in a bag you won't forget is maybe a little more secure.