I would think it would be a nightmare to enforce unless they went with a policy that NFL stadiums have where you pretty much can't bring ANYTHING in but what is in your pockets and a SMALL bag. For a park that caters towards small children (that require strollers, diaper bags, snacks, water bottles, etc.), I would think they would not want to go to a "can't bring anything in" policy ---- even though that would make the park a LOT less crowded inside (imagine the parks if people actually did the parks like they did we WE were young .. no giant backpacks ... kids in either a small umbrella stroller or NO stroller at all??? the walkways would be easy to get through!)).
On a trip in Ocotober 2014 I was traveling with a 2 year old. Because we had a stroller to pretty much carry stuff, we had a SMALL soft-sided cooler bag for a few sandwiches and snacks for a "brown bag" lunch on some days and then we would just have an early buffet (usually character) dinner. It just hung over the handles of the stroller. Keeping him (and us) fed and watered made us have a much better day. Less cranky people throughout.
1) It wasn't really a financial choice as more of a choice to save time. Sitting down and grabbing a sandwich wherever you happen saves a huge amount of time compared to trying to find a quick service .. waiting in probably a long line .. and THEN eating.
2) Depending on the weather (hot, humid) . .I am really not that hungry come mid-day.
On another trip in August, we chose NOT to brown bag it .. as we felt it would be too warm to keep sandwiches cool .. and we would want the lunchtime break to just sit down and cool off. We instead used that space to bring ponchos and "cooling" gear. (both needed).