I have one of those fancy gamer mice (Logitech G700S) and I bound the most prominent thumb button to middle-click. Haven't looked backed, making scroll-wheels clickable was a mistake.

Scroll wheels themselves are a bad implementation of a good idea. I bought a cheap USB volume control knob and used AutoHotKey to rebind volume up/down events into wheel scrolls. Productivity increased like crazy! Scrolling is no longer a chore, it's a pleasure. I even went the extra mile and coated it with rubber for a good grip.

I have always used Gesturefy to make right-click and drag down to open in a new tab. I don't know where I originally picked up this gesture...maybe Opera in 2003? But I've always loved it and use it a hundred times a day.

Why is a 2-handed input better than a 1-finger input?

It certainly depends on your hardware. The GP is just rooted in a completely different experience than yours.