Every summer these stories come out about dog walkers making vast amounts of money while enjoying the sunshine with the dogs, but they don't see the reality, the expenses, the days when we are blue with cold from being out all day, or clearing up vomit and diahorrea, or hoovering up the endless dog hair and spraying for yet more fleas.
If you can keep your dog in sight at all time, be aware of what they are doing and be confident your dog will come back to you promptly when you call, then there is no need to put them on a lead. But if you can not be confident they will return when you call, then a lead is the safest option for everyone.
In my opinion, the coffee cup owners aren't respecting others in the park. They just don't see what they are doing as wrong yet if a youth's dog ran up and jumped up at them trying to snatch a treat it would be totally abhorent. Yet when Phyllis the 5yr old Border Terrier does it, its either not noticed or just midly amusing.