No, the answer is to keep your dogs under control. For many dogs, proper free running is essential to their well-being and the vast majority of dogs are civil to each other anyway.
Keeping dogs on-lead increases the odds of problems as the dogs can't express themselves fully.
Most dog owners around where I live are sensible. I went on a fairly typical off-lead walk at the weekend and I:
Kept my two away from a young dog in training whose owner put her on-lead so she wouldn't get the chance to bomb over and bounce at us (we had a chat from 10 yards distance across the sugar beet);
Called my two in to weigh up a couple of approaching dogs who I was assured were fine, and they looked it, so the dogs all introduced themselves and we continued in our different directions;
Encountered a spaniel we have met before, had a nice chat to the owner while dogs blagged treats off us;
Saw a cockapoo who flattened himself into the grass but the owner said, as I called mine, not to worry, he'd be fine - and he had a very quick play with one of mine and ran off with his owner;
Kept them away from another cockapoo as we went over the playing fields, but only because I wanted them at heel as there was a football match underway close by.
We get the odd brief fracas when a rude young retriever gets in my older dog's face (she tells them to fuck off, they do, and then come back round to say sorry and introduce themselves politely). There's one dog whose owner is insanely anxious about contact between her dog and mine, so we avoid her, and a border terrier who will launch teeth-first, so we avoid both of them. Otherwise, we just keep clear of on-lead dogs and anything being long-lined I less told it's okay.
I get the odd over-excited paw-print on my jeans, and training interrupted sometimes, usually by a puppy whose recall isn't quite going to plan.
Maybe where I live is weird, but it's very rare that we have an issue.
ETA to add, I'm not saying that problems can be entirely avoided by your own dogs being under control - just realise what I said could be read that way. Everyone needs their dogs to be under control and the few big issues we have ever had has been middling or being dogs being dickheads.