I strongly disagree, and stand by my assertion. I've owned dogs all my life (and I've been both very bad and very good at training dogs, depending on which point in my life we're talking about).
I'm absolutely confident that redirection and positive reinforcement is better than punishment...again, so much better that you can accurately say "punishment does not work" without much exaggeration.
Being the leader and punishment are not at all the same thing. Punishment can actually have unintended consequences. If your dog is behaving badly to illicit attention, punishment is still attention. So, the punishment kinda becomes a reward, but it's mixed up with a bunch of fear and confusion in the dog. Now they have anxiety about you, and uncertainty about what the right behaviors are to get the response they desire (attention, affection, food, play, walk, whatever). I've seen so many neurotic dogs who've been made that way by punishment from their owners.
That said, there are ways to not reinforce behaviors (which also work for little humans). When a dog is acting out to illicit a response, the right action is not punishment, but nothing: Withdraw attention. Silently turn away from them, leave the room, stand up if you're sitting with them and they're trying to climb into your lap. This is the same principle as a time out for a child. It isn't "punishment" in the sense most people mean, but it is an effective deterrent to unwanted behavior.
But again, redirection to a behavior that can be rewarded is best. You can't do that until you've trained the dog with a few behaviors that they can be redirected to. Once a dog knows "look at me", "sit", "stay", "down", and "heel", you can solve just about any behavior problem quickly, and your relationship with the dog can always be one that is gentle and free of anxiety for the dog. Dogs desperately want to be good dogs; it's instinctual from tens of thousands of years living with humans. The only problem is they don't understand what "good" means to humans until you teach them, and most behavior problems are communication problems, not lack of punishment.
The notion of "alpha" among canines is so misunderstood by most people that it is kind of pointless to use it as a guiding principle in dog training. Your dogs are part of your pack, not your slaves; they'll do what is good for the pack willingly and happily, as long as they understand what that means.
Perhaps we're just using different terminology here, but when people say "punishment", I assume they mean loudly yelling "no!" at the least and at the worst a rolled up newspaper, or rubbing their nose in poop, a shock or choke collar, or throwing them out of the house, or whatever. I sometimes catch myself becoming frustrated and yelling...but, I have also observed that it does not achieve my goal with the dog, and I can see their confusion and discomfort. In those instances, I should think about how to better communicate with the dog, not double down and become more "strict".
I accidentally adopted a dog recently (long story, but he was an RV park dog whose primary caregiver went to the hospital for over a week during a snowstorm), and he had tons of bad habits from being basically feral. Never walked on a leash, wasn't house trained, etc. It took literally a few days before the neighbors who knew him before I adopted him started expressing shock about how well he was behaving. If you'd told me 20 years ago that a dog could learn to walk well on a leash, come on command, sit/stay on command, be house-trained, and all around be a pretty good dog, in about a week, I would have been incredulous. He may be smarter than average, but really, I've helped tons of friends fix their dog's neurosis. (I am beginning to sound like I'm pitching a dog training program on late-night TV, so I'll stop, but I'm serious. Nearly every dog owner I've ever known is doing it so wrong, and I wish I could fix all of their broken ideas because dogs deserve a good relationship with their people.)