Our last two trips (when DD1 was 4.5 and 6) were stroller-free. It was amazing in every way. I don't really lug any stuff to the parks. The only issue we ever have is jackets. Once she was out of diapers, there was just not much we needed. A small bottle of sunscreen and our credit cards was basically all we carried.
The earlier trip was a bit more of a challenge, as DD ended up on DH's shoulders quite a bit. However, DH absolutely HATES pushing a stroller through crowds and lugging it on the plane, so he was much happier with her on his shoulders. For our last trip, there was no question. I suppose I am the only one with a 7-going-on-13 year old. She would be embarrassed to be seen in a stroller, pretty much since she got to Kindergarten.
However, we went and had a baby, so now we are back to the stroller life for a few more years. I'll console myself by saying that at least I have a place to put the jackets now.