I did this very thing on a Volvo 240 wagon some years ago, except rather than a bolt through the halves, I welded them together. The improvement in appearance was remarkable.

I wouldn't be concerned about being a purist. If you were, you would eliminate the USDOT battering rams altogether and install the original bumpers MB designed for the car (also called "Euro" bumpers in the US). The worst USDOT mandated bumpers however are on the W116 cars. These hideous things protrude almost 2 feet! The second worse are probably the USDOT's bumper bastardization of the W107 cars. In any case, your idea would probably help your car's appearance and still allow the same protection above 5 mph.

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Don't Chrome them; polish them