I strapped mine down differently for my trip out to Moab just because of that. tilt your mirror up and see how often you glance at it. might surprise you.
bolted in place:
ratchet strapped horizontal:
personally I like the idea of the tire being in the bed upright, right behind the driver. takes up a bit of bedspace, but completely out of view.
tire swings can rattle/loosen up, if you build your own, be picky about the hardware you choose.