I'm not sure you can differentiate the horror of what actually happened in Japan with the existential threat posed by the proliferation of thermonuclear devices immediately after the war.
If the threat stayed in the small-kiloton range, I think we'd very likely have seen them used again -- especially if one nation had a monopoly on such weapons.
But that's just a supposition; in the real world, we went from "there are two bombs, and we used 'em on Japan" to massive proliferation of weapons orders of magnitude stronger by opposing superpowers in a really really short period of time.
I was surprised to learn, in the wake of online discussion after the release of OPPENHEIMER, that the weapons on hand now in the US (and assumed in the former USSR) are actually much SMALLER in yield than what was on deck from the late 1950s through the mid-1970s.
The Nagasaki bomb was ~ 22kt.
We (the US) built a 500kt fission-only bomb (the Mk. 18), so 20x that power; that was thought of as the functional ceiling for a simple atomic bomb.
But then came Teller-Ulam and the mk 17 thermonuclear bomb (no, I don't know why it's a lower number; maybe they started over with the thermonuclear devices?), which came in at 15,000 kt. A linear-scale graph showing Trinity, the Mk 18, and this bomb is hilariously inadequate; it's an object lesson in how warping it is to consider enormous numbers.
But with more precise delivery, and a large shift to multi-warhead ICBMs, the actual individual device yield shifted downward. There wasn't a need to fudge your margins with huge bombs if you could be reasonably certain of hitting a given target. Further, hitting anything with 15,000 kt would be absurd overkill unless your whole point was to wipe out an entire population center.
The biggest active US bomb is the B83, at about 1250 kt, or an order of magnitude less than the Mk 17. It's a gravity bomb, ie, requires a bomber. The bulk of the arsenal is, I believe, still tied to ICBM delivery, and hover under 500 kt per warhead (W88 in the Trident II; W78 and W87 in the Minuteman).
At first blush, the idea that we aren't arming ourselves with 15,000 kt weapons anymore SOUNDS good -- except analysts worry that less terrifying yields makes them more likely to use.
I'm paraphrasing from an excellent Twitter thread from nuclear weapons policy & history analyst Andrew Facini at