One more point about those big, scary animals. They aren't tame. They fight along side you and kill for you. They aren't trained. As a general rule they are wild creatures who have agreed to walk by your side because they find something in you and your understanding of nature that's worth their while. If some child walks up and pulls on their ear, they will retaliate, they may even kill said child. It will happen far too fast for the druid or ranger to stop. The creature will feel pain and they will respond. They won't even necessarily understand that's a 'cub' that they just killed, and as such be remorseless. In other causes, they won't care even if it is understood to be a 'cub.' Law of nature, the fittest/strongest survive. An event like would cause the guard to hunt down and kill your animal companion that you care so much for. As a druid or ranger or mage of at least average intelligence, you would know these things with out having to experience them. Would you want to put your family/friend/companion in that position?
I'll have to disagree on this one. Despite the fact that we don't see them, commoners surely sees the adventurers on a daily basis. Sure they can hear that there is one bad apple somewhere, but there is one simple thing called accustomisation.
I'd just like to point one thing that I think has been missed. An animal companion or familiar has an empathy connection to his owner. If the owner is calm paused and secured, the companion or familiar would sense it and it would certainly have it's effect on it. So if the owner presence calms the animal ( providing the owner is calm himself) then even if a kid ran yelling, it wouldn't take long for the owner (sorry to use that term, as they are not owners but really more symbioses) to calm them.
As for people running in fear, I'm not sure, but if we take history here, there has been rural performers with animals, big or small, throughout the ages. Now we could (by judging of the settings) assume that this is medieval (pre medieval?) times, and performers were quite common, going from city, big or small, to do their shows. Granted most of them were leashed, but people would be somewhat used to it.
Also this being a fantasy world, we have to take into account that the commoners are aware of the rangers, druids, and mages (including sorcerers in there for ease) abilities to connect with their animals. They would most likely be able to recognize a ranger and druid, when they walk into a town> And so would have a certain re assuredness when they see their companions or familiar (for the mage type) with them