Because of these reasons, I choose very carefully what park, and where, depending on condition of grass and how often it looks maintained.
I wouldn't like anyone digging up my nice clean turf that I spent hours keeping.
Under trees is an obvious okay due to grass not growing.
I don't like to do sporting fields, I don't think its a good idea to leave divots. No matter how well you plug, it will always sink slightly.
So if I do sporting fields, it is with no digging tools, just for modern surface finds only, the coins that tuck in under the grass.
Kinda sux because it leaves out a lot of the good areas, but I guess that is also part of the hunt. Trying to find the right places.