Unfortunately I’ve only ever experienced it in my own little software experiments, because there’s no obvious way to splice it into all applications at the OS level. If you control the hardware/firmware on your mouse/keyboard/trackball then you should be able to make it work, but it might not be easy:
It was ten years ago I last checked so I might remember incorrectly or things could have changed, but I think that you could rewrite the generic mouse driver on Mac to get button mouse-scrolling. It is part of the low-level Darwin framework, which is Open Source.
As a matter of fact, mouse-button scrolling was one of the reason why I wanted to hack Mac's mouse driver in the first place. However, I decided to instead sell the Mac and go back to Linux so I never finished it.
I had wanted to make it feel like middle-mouse-button scroll in Postscript viewer "Ghostview": instead of a direct translation of movement to scrolling, holding down the middle mouse button would extend a movement vector: the length of the vector would tell how fast the scrolling would be.
Some web browsers do something similar, but they toggle scrolling mode instead of doing it the right way: there should be scrolling only for as long as the button is held down.
Am I the only one that still uses page up/down and arrow up/down? I've always found that to do the job.
That is what I always use. The scrollwheel has been removed from my mouse.