I am bringing up World War One, yes, because the point was made as if the iron cross is somehow more benign than the rising sun.

The Japan of WW1 used the exact same flag and symbols while fighting for the allies as it did in the second war and continues to use today, while again being aligned with those same allies who are still using their symbols. They are enduring symbols of their nation, and I imagine it simply doesn't strike the Japanese as a necessity to change them out of remorse for an imperial past, any more than the British would consider dropping the union jack or America the stars and stripes.

To your second point, there is absolutely something China could do about it, as evidenced by Korea a few years back requesting that Japan not fly the naval ensign on their ships during a naval review, and Japan withdrawing from the review. The issue over the flag seems to be a uniquely Korean point of contention given that Japanese ships regularly call on ports throughout their former victims in the Pacific without issue, but if countries feel strongly about it the precedent is there refuse entry to Japanese ships bearing the flag.