Where I am working everybody has to be certified. That includes everything from skid steer loaders to cranes. And also all of the other stuff like Hilti guns, confined space, fall protection etc.etc.
For all the OSHA 40 hr, HAZWOPER etc. we do it on line. The heavy equipment certifications are performed by a 3rd party.
A lot of municipalities are requiring certification too. Although in this case, I have only seen it enforced as a result of vindicitiveness on the part of the 2nd low bidder.

I recently had to rent a small boom truck and was told that they couldn't rent it unless I had a CDL (I do). It was on a two ton truck frame which I know doesn't require a CDL. It just made me realize that I actually don't have certification for some of the equipment I operate.

I think it comes down to a cover-your-ass situation. If you get hurt, hurt someone, or beak something, you can claim you weren't "properly trained" and sue. By requiring certification, their ass is covered.