Just thinking about Jeff Slotkin's comment on the "spokes on the chainstay" idea for protecting the paint and/or chrome down there.. I reckon if my chain was rubbing along all those hundreds or thousands of times I would either invest in a chain rivetting tool and shorten the chain, or check that the tension spring on the cage on my rear derailleur was still working OK..
In reality whether you've got a rubber band, a leather strap or the spoke set-up, they should only be in use when removing the rear wheel, or on those "bouncing chain" occasions such as on the pave or other pretty rough road surface.
Norris Lockley .. Settle UK