For dogs that have become difficult to handle due to incorrect early training( by any method incorrectly applied), genetics etc one then has to sort through what is likely to have the best outcome and find someone skilled to teach you the way forward.
With the help of an experienced trainer who specialised in more positive methods - I rehabbed a very fear aggressive dog. The method I used was based on positive reinforcement. Key to the success was timing, setting the dog up for success and always working under threshold. I didnt have to withold things because I became skilled at how I set her up and how I reinforced her and at recognising her thresholds and her body language and reading situations. She got so much well timed reinforcement it completely rewired her outlook. It was very hard work because this type of method relies some intensive learning by the human, you have to be totally committed and have the guidance of someone who knows what they are doing.
There are plenty of tools in positve but you have to be committed to really understand how to use them. Problem dogs can be rehabbed this way, but it is never for the faint hearted. It is not rainbows and sunshine, it is hard work, behavioural science and the handlers ability to work with those tools.
I personally have never had to withold stuff to make a reward valuable for any of my dogs, they have always been driven by toys etc because I played so much with them as pups and instilled the love of play and tricks. Reinforcing all the time what you want at any any moment when you see it. Down the track you may at times have to withold a reward but it is very rare if you have trained the dog to work in a certain way. They come out raring to work for you with so much joy.
However neither am I against the used of more physically corrective methods if they are trained properly. Like with the use of positive, timing is always the key. I am not skilled in training this way but I would assume that the well timed application of low level correction and release to a dog who is under threshold and learning is way more valuable than harsh corrections and yanking and cranking of an over threshold dog unable to really process any learning. There is a lot of skill in any training method. Unfortunately a lot of people dont really understand it and when faced with a difficult dog will often come unstuck which results in bad press for both positive and physical corrective methods.