The only reason the "American style" exists is a technical workaround: It was easier to damage the expensive lead type used in print shops a century ago if the thin period character was used on the end of the line, rather than the thicker, sturdier quotation mark, so they were swapped as a cost-saving measure.

None of this has been relevant for many decades, and people have forgotten the reason for this rule. It was never correct to do, it was a choice to do it the wrong way around out of convenience.