> How many good people were discouraged into going into this area of research because of this widespread belief that this pursuit is proven to be unachievable in the general case?

You need to read this book:

https://www.amazon.com/Quantum-Computing-since-Democritus-Aa...

(The title notwithstanding, this book is about a lot more than just quantum computing. In particular, it is about computational complexity theory, which is exactly where your line of inquiry leads. It is a very productive area of research.)