Everything you said is true, however:

The best camera is the one you have with you.

I, for one, don't carry my DSLR with me everywhere, but I almost always have my phone. I'd like to know that I'll be able to get something when that one-in-a-million shot presents itself.

For me, I take my DSLR out when it's my intent to do photography. When I'm doing something where I think something might present itself (e.g., on my bike), I carry a compact camera if I've got room and won't endanger the camera too much. But I'll almost always have a phone with me.