For years (many years ago) I took my dog Dutch to a local park. He heeled all the way there and all the way back. Once at the park I took the leash off and gave him the command “way you go”. He took off at great speed and circled the park until he exhausted himself. When (and if) he pooped I used a baggy and cleaned it up. Thoroughly. Pooping was generally reserved for the backyard where it got the same treatment and where my kids played to their hearts content.
If a dog is trained, can demonstrate constraint and listens to commands, he should be able to demonstrate it to authorities and be rewarded with a special tag, and then allowed to roam under supervision.
All others should be limited to a fenced dog park – which ain’t a bad alternative, but it’s not as good as an exhausted dog coming home to lots of water, a few treats and a soft pillow.