I see there is a large degree of miscomprehension of what positive reinforcement is. The addition of a stimulus that increases a behavior.
Positive reinforcement works so well because it *has* to be something the dog wants more of, which they seek to earn from you. I've seen people force their dogs to earn things the dog doesn't value (praise and pats only, mostly) but that's not positive reinforcement, that's a safety signal that a correction isn't currently forthcoming.
Food is just the very tip of the quite large iceberg. Food is not the end all, be all of positive reinforcement, although usually food works very well because A. Dogs, like all of us, have to eat and we ALL work for our food to some degree besides children and pets B. Healthy dogs enjoy food, especially when they get to play with their food (please Google the term "contrafreeloading"), and C. Food can be divided and easily parceled out, making a high rate of reinforcement and frequent training sessions possible (keys to success).
Food can be regular meals, or low calorie treats, or higher calorie treats and reduced meals on training days to compensate for this. Dogs only get fat if their food isn't managed well by their provider, or they have health issues.
The list of positive reinforcements are individualist but possibilities are endless: toys, attention, scratches, Premack Principle (this is one of the most powerful ones right here), sniffing a hydrant, greeting a neighbor, going outside, chasing or being chased, tugging, smelling hunting odor samples, conditioner reinforcers, secondary reinforcers, primary reinforcers, tertiary reinforcers, etc.
The most famous working dog organization, Guide Dog for the Blind, is moving away from punitive training and punitive tools. Most service dog orgs have or are. Even military and police dog departments are. Some entire countries have, and Steve White is quickly becoming a leader in K9/military dog training here in the USA (the USA is behind most countries in training standards).
I'm a service dog trainer myself, I also specialize in rescue animals with severe issues. This is not limited to just dogs, I train many species. They don't make collars for these species, and you won't walk away unharmed or even alive if you attempted to train them how the domestic dog allows themselves to be trained.
Humans have hands and dogs have their mouths. Just like human children, puppies aren't born knowing what's appropriate to their owner/parent and what's not. Puppies play bite. It takes time to learn what their human prefers. Especially since they don't get to spend a lot of time learning bite pressure inhibition from mom and litter mates by the time most are sold.
Every single person I know wants patience, empathy, and to be treated well when they're learning something new, or have an emotional issue they're trying to work through.
Learning and behavior modification, done properly, rarely is instantaneous. Instant means subduing symptomatic behaviors but not addressing WHY they're happening. Learning takes time.
Why we won't extend the same courtesy, that we would want for ourselves, to our animals that we choose to place into our own homes, is beyond me.
Pinch collars work because they hurt. It's simplistic and quick. An "easy fix" that's just a cop out. But it doesn't teach your puppy much beyond the fact that you'll hurt them.
What people feel they should do is up to them, but correctly utilized (it has to be done correctly) positive reinforcement works. And it's pleasant for our dogs, and it's healthier. Chronic distress is very hard on the body. My service dog and love of my life worked up until she was 13. I recently lost her at 15 and my heart is broken, but I can at least find comfort in the fact that she knew that I would never do anything to hurt, scare, or intimidate her.
Personally, I don't like to distress my animals, I'd much rather choose training they enjoy instead. I enjoy it too. I don't enjoy hurting, scaring, or intimidating others. Especially helpless animals and children at my mercy.
If positive reinforcement didn't work for your dog, then I'd suggest hiring a competent force free trainer who can share their expertise with you.