Sorry, but aside from an occasional guy pushing an ice cream cart, I do not normally see vendors at local parks in United States. I recall once I was solicited to buy firewood at a county park, but when those guys saw the park ranger coming they drove away. I cannot think of a single instance when I saw a bolted-down structure selling food or anything else in a park, or anything with commercial signs. Those belong on a regular street in a business district.

The closest I've seen to what you're describing is designated areas for food vendors at county fairs, food trucks at swap meets, and vending machines near the restrooms at highway rest areas.

Regardless of the "rent", I do not see how shipping lockers are appropriate for a park. Even the post office does not put mailboxes inside a park. And if this is OK for Amazon does that mean UPS, FedEx, AliBaba, and whoever else can join in??

Yes, this is what corruption looks like.