They weren't just seeing if they worked. They were interested in being able to calculate the reliability of them (which takes more than one or two), they were interested in variations and tweaks, they were interested in refining their understanding of what was happening (e.g., if you vary the boost gas by X amount, can you predict the change in yield?), they were interested in loads of effects tests (not just devastation, but complex things like how the EMP interacts with electronics), and so on. And they weren't testing just finalized devices; they were testing out different primary ideas, different secondary ideas, and so on.

If you go over the individual test series, you can get a sense of how the work was done, like this one of Operation Dominic. They were all over the place — new concepts, new primaries, slight tweaks, what have you. Even a full-systems test (mated a warhead to a missile), which was really a reliability test.

Now, was this overkill? The scientists could justify it all as science. Science isn't about testing something once and seeing if it's true, it's about getting such a detailed understanding of nature that you can make predictions about it, know exactly what your error bars are, and have real confidence in what you're doing. So the scientists would say, no, this was all about making sure that these weapons would work exactly the way they were supposed to, no matter what, and also give the US or USSR the capability to adapt to new situations (like moving the tests underground, or stopping testing).

But that might not be the right question to ask. The right question might be, could they have a credible nuclear deterrent with fewer tests? And the answer there seems to be, certainly. I mean, everyone else seems to have done it! But that isn't the mode of thinking the US or the Soviets got into — the culture of the laboratories, and of the US nuclear weapons establishment, became one of striving for total knowledge, total control, total confidence... and that means a lot more work than "good enough."

So could they have gotten away with 10X fewer testing? Sure. They probably could have gotten away with 10X fewer weapons, too, if the goal was just deterrence. They had loads of essentially redundant systems. But stalemate was never just the goal — the cultures that drive these arms races are never about being satisfied, and everything about being unsatisfied. They thrive on that dynamic, on the need to always change and improve, to do more testing and field more systems and have more spending. They are suspicious of arms control exactly because it is stabilizing; they resent it and consider it stagnation. They constantly fear that the enemy is doing more, and so want to push ahead, even when they know that this will guarantee that the enemy does it own work as well. It is an impulse both paranoid and expansionist, and if it's in the driver's seat — which was the case in much of the Cold War, and is increasingly the case today — you see a lot of what looks like "unnecessary overkill," as you put it, in retrospect.

If I were to recommend one useful book for understanding how testing and laboratory culture worked in the late Cold War, Hugh Gusterson's Nuclear Rites, an anthropology of the Livermore Laboratory done at the end of the Cold War, is what I'd offer up. I also think Donald MacKenzie's Inventing Accuracy, a historical sociology of missile accuracy, is very telling on these points. For capturing the mindset that enabled these kinds of regimes to thrive, Eric Schlosser's Command and Control is a good, accessible read.