>normally won't kill or majorly injure the other dog but mainly make it submit
some are doing it by biting and sinking their teeth deep into the back of the neck of the victim. So it does make sense to step in before that happens, as well as to step in to stop that when that is already going on (i've met owners who had that happen to their dogs, and couple times i stepped in right before that was going to happen to my dog)
(Which I am not!)
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>that happen to their dogs
It's a pretty normal part of dogs inter-social behaviour, as you should now the back of the neck of dogs is used by parent dogs to discipline (and sometimes carry) their pubs. In turn it's also used to make dogs submit in social fights between them. Which is a normal/natural part of there social interaction.
And yes there are aggressive and dangers dogs, too.
Still if you step in you are likely increasing the aggression the other dog has against your dog. Which if it repeatedly happens with the same dogs could make the situation problematic if you at some point are not fast enough to step in.
i understand that you describe a consistent and logical model. Unfortunately it has nothing in common with the reality i know. In one case it was a large labrador - a lot of muscle on hit back neck - so he got an inch deep wounds, a lot of stitches and drainage for a week, in another case it was Chihuahua - not much tissue - so he ended up with a series of surgeries on the bones and cartilage in his shoulders.
It's not just a risk for you but can also make the dogs involved more aggressive.
Furthermore most dogs (which do not have mental issues or are badly wrongly trained) normally won't kill or majorly injure the other dog but mainly make it submit. But if you step in thinks can still escalate.
Lastly the problem are not dogs of the leach, but people not training their dogs properly (and often not understanding/ignoring that they don't train their dog properly). Or people buying dogs which are bread (and potentially even trained) to be super aggressive. Which IMHO is a no-go and requires the dog to muzzled nearly always outside of private properties (through ONLY for this dogs bread to be aggressive, e.g. for dog fighting).
I have been in areas where dogs are allowed to be of the leach frequently and is generally not a problem, most dog holders living around where I live do not use a leach when walking their dogs in the evening and it's not a problem.
EDIT: Wrt. the main thread, if you dog is properly trained you can have it walk alongside you without a leach even with birds close by and it won't run to the birds. A lot of dogs I meat are good but not hat good trained so while there really is no reason to put them on the leach in the city or common German forest areas you would put them on the leach if you enter a area with e.g. ground breading birds.