I think it really depends on your situation. I live in a big city, and we walk a lot for errands - post office, health food store, etc. We have a fairly big stroller that we keep in the entryway for these walks, and we use it frequently. My son is 2.5, and he started not liking the bjorn or sling at around 1 yo. Before that I much preferred to carry him.
I keep a really small umbrella type stroller in the car just in case. Mainly because ds likes to go running off from me, tearing stuff from shelves, and dashing behind aisles thinking it's funny that I can't see him. So on rare occasion (less the 1x/week) I use the stroller when we are out and about. Honestly I use shopping carts more. Even if I don't need one, I let him ride in the big section and I push him around.
And when he was an infant, although I did use a bjorn or sling whenever he was awake, I definitely got a lot of use out of the carseat that snapped into the stroller frame. I know a lot of people get uppity about these 'baby buckets', but I don't care. My ds would fall asleep in the car every time, could not be transferred without being woken, and would scream bloody murder if he was woken before he was ready. So to be able to still stop at the bank or the store and just grab his carseat with him sleeping was a lifesaver.
So yes, I would need a stroller. If I were in a more remote location, I would probably only have a smaller one in the car for very rare use. But in the urban lifestyle that I live, the stroller has definitely come in handy.
I am jealous of moms whose toddlers still like the sling. Mine would wriggle and kick after about 5 minutes. Plus he got heavy. Carrying him in a sling while wriggling and whining, and two bags of groceries, uphill 6 blocks back to my house - no thanks.
And I have never put ds in the stroller if he doesn't want to go in, and have never left him there crying.