I have two children, two and under, and I don't use a diaper bag.
It's true, and it's amazing. I use my now four year old, Marc by Marc Jacobs Classic Q Hillier Hobo. I used the diaper bag I purchased before having Ashlynn, a Nest Hudson diaper bag, until she was around 8 months old and then pulled the switch-a-roo. I'm pretty sure it all happened the same time we switched from the infant carrier to the convertible carseat.
I still have deep feelings for my diaper bag, really the only drawback in my opinion is that it's big. Which is also it's greatest highlight. You can see it's size on me here. I think once I was carrying her to and from the car seat to shopping cart, I asked myself why am I carrying this giant bag to the grocery store, when I never need any of it's contents other than my phone, wallet and sippy cup? I soon realized a smaller bag with just the need-now essentials could get me by.
Of course, that list of need-now essentials changes every few months, but I've been able to manage the change from baby to toddler and even the addition of a newborn to infant all without having to add a giant bag back to my routine.