That is a terrific idea. Years (many, many years) ago I built a behemoth bumper and hitch affair for the back of a 4X4 truck. I cheaped out with a piece of 2" (ID) square tube I found somewhere for the receiver hitch. Trouble was it was slightly oversize and any hitch I put in it slaped side to side and up and down. I ended up fabbing a three sided shim piece that I slipped in around the hitch to stop the slop.
I like your idea but might point out that carried to the extreme a fellow would do two nuts and two bolts. One in each axis, left/right and up/down.
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