I haven't read all the replies, so I have no idea what's been said so far.
I have a 1 year old (non-walking) son who rides in a stroller, or in one of our baby carriers (Kozy, Peanut, etc). I also take care of a two year old little boy who walks when we go places. I am looking into a double stroller though. He can sit in the Kozy, but wants to explore. I'm okay with that. But sometimes he gets tired, sometimes he's just getting into too much (i.e. running through Hallmark in the mall trying to knock glass figures off the shelves) and I don't feel like messing with it at the moment. But normally he does walk and explore. We go out FOR the boys. I want them to learn about the things around them. Be that at the park, mall, zoo, Target, whatever.
There's not a thing wrong with a 4 year old being pushed in a stroller. But it's also not something that would often happen for us. They are big enough to walk without tiring quickly. We don't stay out long enough for a 4 year old to tire out. Now, at an amusement park, the zoo, things like that, I would plan for a four year old to ride in something. I wouldn't want their little legs and feet to start cramping and all that.