What if the .01 K yield W54 A-bomb had been used regularly in armed conflict?

https://en.wikipedia.org/wiki/W54 The smallest A-bomb ever developed was the W54, in the late 1950's, with an effective yield as low as 10 tons of TNT in some versions. Hence, there are actually conventional weapons with a larger blast than the smallest versions of the W54 nuclear bomb. As such, it is clear that unlike most nuclear weapons, the .01 K version of the W54 could not possibly be a threat to the survival of human civilization, unlike larger nuclear weapons. Now, there certainly exists a kind of psychological taboo by this stage implicit in the human psyche, that we must never use nuclear weapons again, because the entire human species would be destroyed, or, at the very least, reduced to a paleolithic existence. However, even if thousands of .01 K W54's were deployed and used in armed conflict, it is unclear how they could possibly have this effect. Indeed, it is unclear that such bombs would have significantly affected any of the armed conflicts that occurred since they have been developed. What, exactly would be the reactions of other countries to U.S. using the W54 in a war? Or, for that matter, how would the U.S. react to other countries using such a low yield nuclear weapon in an armed conflict? Surely, this would not unleash Armageddon? Why would it? How would it be more of a threat than a comparably sized conventional weapon? Even the radiation would be almost entirely dissipated after a few days. Now, of course, one could argue that the use of nuclear weapons is a slippery slope. That once a very small nuclear device was employed, we'd soon be throwing Tsar Bombas around. But, surely, this is not inevitable. I would suspect, rather, the main effects would simply be that the development of nuclear weapons would be turned over to the private sector, as with conventional bombs. Now, this could present some security concerns. After all, even a small A-bomb could be used, in combination with Deuterium that can be extracted from seawater, to build H-bombs of unlimited yield. However, bear in mind, the new modular designs for small atomic reactors, if widely used, would have quite similar effects, making plutonium readily available to the private sector. Thoughts?