If it nothing but light powder, you can push snow with the bumper and never have a problem. If it's heavy and wet, that's another story.
Yeah moisture content in the snow plays a big part of it. But even if it's dry powder snow with very little moisture in it, and other vehicles have driven over it a few times and packed it down a bit, chains will really help you then also.
We don’t get alotta powder around my area it’s mostly heavier stuff. There was about 14-15 inches where we went. I’ve never tried pushing through more than 28 inches of snow but I haven’t needed the chains this far. I have memory’s of helping my grandpa install & uninstall chains and they are painful
kinda turned me away from them. I’ve also seen chains tear stuff up on vehicles multiple times.
If you don't keep tire chains tight, and allow them to get loose, then they can tear up stuff like fenders or brake hoses. Or if you drive way too fast with chains on, they will get loose and then tear up stuff. If you are sensible when they are on, and you have the right size chains for your tires, and you keep them tight, there's no reason they will tear up anything.
I know for a fact tire chains have saved my life 3 times. Where I either would of been staying where I was until help came along if they ever did come, walking for help 25-30 miles, or living & camping out where I was until spring thaw. Having a set of chains those few times, saved me.
Most all western states I know of, have chain laws for commercial vehicles. If chains weren't necessary I doubt they'd have those laws. I've sat on a highway many times in heavy wet spring snow, where there's no place to go, for up to 8 hours, in the central Rockies on the backside of some 20-30 car pileup, all because some bozo driving a commercial vehicle thought he could make it over the pass without chaining up, when the chain up sign was flashing, then he created a wreck. That ruined more then just his day.