I volunteer at my local shelter and see these dogs first hand. I know exactly why they end up in shelters and some of those reasons include their owners feeling like failures because their experiences are that they put in what they feel is a lot of work and see no improvement. Actually, most owner relinquished dogs, vs stray pick ups, are because the owners have reached a point where they have become overwhelmed with behavior issues they are having. Many feel that they have given an honest try at tackling their dog's issues.
Our shelter has seen a very positive response by owners when they are provided with resources such as contact information for local trainers who do consults to help these owners work with their dogs.
Yes, there is a huge homeless animal problem in this country and though there are some who truly don't want to be bothered to do the work that it takes to own an animal, a much larger segment just needs education and access to resources including low cost vaccinations, training programs, and general pet ownership education.