unclear on the concept how is the leash punishing the dog. Perhaps you have confused the advice. Nipping and mouthing are often attention seeking behaviors. Many of those that advocate no physical punishment still use punishment.
In behaviorist term if you add something it is positive (plus for adding) and if you remove something it is negative. You can reward a behavior or punish a behavior and when you do so you either add something or take it aways. So positive punishment means you add something to punish the dog like a swat with a rolled up newspaper or you can take something away like your attention and that is called negative punishment. This is what is used by so called "reward/praise based" trainers. The leash in this case is a tool to accomplish the isolation. It does not really matter if the dog is taken away or the people leave, In the case of a single person it is often eaiser to isolate the dog where he is, in a family situation it is often easier to move the dog.
Another varriation on this theme is
You won the Prize which is useful for those that have a hard time punishing a dog. You do not punish the dog - nope - instead you reward him with something he does not want, happily and cheerfully. Dog nips yippee he gets quality time alone away for the rest of the family. Dog pulls on leash - yippee he gets to go in the opposite direction. For many it is easier to be consistent rewarding the dog for a behavior. If that is the case "you won the prize" is for you.
I am skeptical that \"time out\" which requires reasoning and logic would really be effective for training purposes
A but it does not. You must consider the behavior and the cause. IF attention is the cause of the behavior then that behavior is much less likely to occur if it has the complete opposite effect. For social creatures issolation can be a very forceful punisher. One must be careful what we often consider punishment the dog might find rewarding. Dog jumps up for attention, We swat dog on snout, push dog away, hollar at dog, quess what we just engaged and interacted with the dog just what he wanted. better to turn your back on the dog and leave. As soon as all four feet hit the ground and stay there reward the dog.
The one problem I do see in timeout is when you must interact with the dog to administer it. Fumble to but the lead on etc. The dog should have the lead on already or at a minimum a short thab that can be used too take the dog into the issolation area quitely, calmly with little or no emotion. This can be very hard to do, it is why many find that instead of looking at it as punishment consider it a reward for that behavior. The one caveate that a dog that spends most of its time alone may not find issolation much of a punishment. Every dog is different, the thing with punishment is excluding extinction burst which come from ignoring behavior if it is going to be effective result are observable and a reduction of the behavior happens quickly. If not the it is not punishing to the dog. Again the exception is ignoring behavior which at first will have the very opposite effect> Just like the light switch, every time you turn it on the light goes on, then one day you flip the switch and the light doesn't turn on what do you do. Say oh that doesn't work and continue on your way in the dark. Or get a bet fustrated that it doesn;t work an flip the switch again and again and again. maybe a little faster, no - how bout slower no push the swtich a little left, a little right ok the switch doesn't work. You may ever once and awhile try it just to see if it works. If it does you back to using it again. if not it will be even longer before you try again. People that don'k know about or understand this phenonom see the behavior getting worse assume ignoring the behavior is not working aand go on to try something else whien in fact this sharp escalation of the behavior is actual a sign the method is working.