With my 6500 4wd, I was able to dig out my pond during the drought getting ready for the next rain. The 4wd was absolutely necessary to back up the grade with a full bucket. I think FEL work benefits from 4wd. Heavy uphill backing, like digging any big hole, will need 4wd.
Your 6500, just like the new 30 series and 60 series, have massive front axles and planetary gears, etc. So you can get away with this, but we actually see people breaking front axle parts if they do this a lot. What happens is when backing up hills with a big load in the bucket, your back end is light due to the angle and the load, and you are asking a front axle designed to be only assistive to move the entire tractor with a load, up a hill, probably in soft soil. If you pop the clutch carelessly, then one of several things must happen. 1) Everything holds (like on your 6500) and you just simply back up the hill but put a huge strain on the front wheel assist system 2) The front tires spin, and they won't want to with all that traction 3) the clutch slips, and that is not likely 4) you break an axle shaft or driveshaft couple or gear in the front end.
Even on a compact tractor, a rear axle might be 2" in diameter, the front will be half that. Likewise on the ring and pinion. They are designed for the rear axle to do most of the work moving the tractor.
We all do this sort of thing, but I'd recommend to folks that they be gentle when asking the front axle to take those kind of loads.
I think one huge advantage of 4wd is brakes. When going down a hill in 4wd and you hit the brakes, the front axle is mechanically connected to the brake system in a round about way and you essentially get front brakes. That is a huge advantage. It's a scary thing going down a hill with a full bucket load with a 2wd and realizing that your rear tires are barely touching and you essentially have no brakes.
