Is overheating the only risk with the neutral conductor and triple-n harmonics?

By far not. But first of all it needs to be pointed out that only very few fires are clearly attributed to current harmonics and overloaded (possibly downsized) neutrals. Unfortunately insurances hardly ever investigate the precise causes of electrical fires. If a cable or distribution panel goes on fire, this is booked in the statistics as an electrical fire and the damage paid for, and that’s it. But even far below the threshold of thermal overloading the effects mentioned under the question about the assumed advantages of a TN-C system start to become detrimental. For a curious example of electromagnetic interference accounting to voltage drops in the lines but far below the thermally relevant level see next question.