I read a leash as maybe saying, "The owner doesn't trust this dog unleashed"; and no-leash as saying, "This is a well-behaved dog."

That's if I can assume that the dog-owner is competent.

IMO it's just as good (as using a leash) to demonstrate your control by giving "sit!" or "heel" or whatever else. Ideally your dog is looking to (looking at) you for instructions, in which case I can ignore the dog and talk to you. If the dog is looking at me and trying to make its own mind up, then maybe I'll avoid all y'all (so that the dog stays closer to you than to me).

The important thing (the only important thing) is to be safe. It doesn't matter so much whether I'm scared of the dog and/or want to talk with you, the most (or only) important thing is that I mustn't be attacked.

I tend to use a leash only for safety's sake (not to punish the dog, not to make people feel happy) and/or to comply with the law.

The other bit ("homeless, long hair, unshaven, muddy") is maybe a bit more important than the dogs.