What is the most basic fault with leaders not extending on a cast?

I have used tapered leaders, knotted leaders (Orvis etc.), and tied my own according to various formulas. I have always had problems. The first problem seems to be getting rid of the built-in coils.
I've tried rubber straighteners, plain stretching and using hot water. These just don't do it.

Even when the leader is straightened it seems to resist carrying the fly out.

Please don't suggest that the only solution is to use the latest and greatest of some new product. Fly casting has been done for decades before the advent of most of these things.

Thanks .