"There is lots of abrasion in a dragging situation, such abrasion would destroy the strap."
Yep....straps won't work...they are great for towing though.
Chains don't take too much of a hit, unless you're dragging across stone or something harder then the chain. Also...if you can find some worn out firehose, run the chain through that. The hose is sacrificial...also, should a link let go, the fire hose will reduce the snap back. If you live in an area that depends on volunteer fire fighters, getting old hose isn't difficult. 1½" hose works great.
Personally, since I don't skid trees (mostly fallen branches and such) too often, if the load isn't too great, I pick the end of the tree or branch up in the bucket and use the chain to rig it for skidding. I'm normally going across a finished lawn, so this method minimizes the ruts. This method is not for heavy loads...that's what the draw bar is for. Also, one of our TBNer's can attest that the front assist gears in a 790 cannot take as much load in reverse as they can driving forward (busted the gears in the front differential).
For a residential operator, the 5/16th's chain sold by Harbor Freight will work fine. I'm a residential operator...this is all I'll need.
BTW, I would hesitate using this chain for tow a vehicle out of a ditch...but common sense will tell me when the load is too much.