I never heard reason #2 claimed by anyone of standing in either PL or OL.
The best lifting coaches and docs in the US are at the Olympic Training Center in Colorado Springs, and a look around the facility shows belts everywhere. In OL, I doubt they'd even let you train without one.
10-4 on leather over nylon, but care is important. The leather must be kept water-resistant or it will become sweat soaked repeatedly and stink to high heaven plus get moldy. (Impossible to un-do) Lotion type treatments will soften the leather and let it stretch, though, defeating its support function. Answer? Use only a paste-style, wax-based treatment like Obenauf's.