I vote a solid (and unpopular) no. I have been at the park with two kids (from ages 1 - 26). We brought a stroller on one day and one day only (the year we had a 1 year old and a 6 year old). I almost ditched it in the park. It made everything so much more difficult. Maneuvering, parking, people wanting in, people wanting out - misery.
Before we had the younger one, we had been three times with my older daughter (she was 2, 3 and 4). She walked most of every day. We gave her a bag of skittles - as long as she was walking, she could be eating. We carried her every now and then - mostly after parades and fireworks. The younger one had more energy than all of us - she never complained about the walking.
We also do not bring a lot of stuff into the parks. Back then - a small backpack with a change of clothes for the kids and a diaper or two. That's it. I never feel that we are going off into an abyss - so I can buy something if I need it. Which - thinking back - I never needed to do except for food. I am not lugging lunch into the park. That is not my definition of a vacation.
Also - I think you experience the parks more with your kids if you are walking along, holding their hand and talking to them. Pushing them along in a stroller while they suck on a sippy cup in a crowd of people - I don't get.