Whey protein is not a supplement.
Whey is just another form of protein. Just like beef is a form of protein (and fat, minerals, etc).
Whey protein is a food like anything else.
Your second to last sentence is based on a false premise.
I also dont see how the milk analogy is relevant. Saying 'whey is just milk without the carbs' is like saying 'diet soda is like regular soda without the carbs'. That's true, but that doesnt make them similar. They are two very different things.
With all of that said, I dont think OPs idea is good at all. But as far as body composition goes, there probably isnt going to be a problem.
I also dont think eating chicken all the time is a good idea.