Your assumption is incorrect. In the 1950's the US Army developed and deployed two variants of the Nike Zeus ABM armed with an atomic warheads but when the USSR went all out in developing & deploying hundreds of ICBMs, the costs of trying to protect the entire continental US became untenable and the project was shelved. But the effort to protect the US from Soviet ICBMs didn't go away. In the 1970's the Sprint missile was developed with a low yield radiation enhanced thermonuclear warhead but its active deployment actually only lasted less than a year. The 1962 Starfish Prime nuclear test in space over the Pacific which produced an unexpectedly large EMP that disabled several satellites & disrupted telephone & electrical services on the Hawaiian Islands (over 800 miles from the detonation point) showed that using nuclear warheads on ABMs was not an optimal solution and eventually led to the development of the kinetic kill vehicles that are now being tested.

I was working as a still photographer at WJLA-TV in DC and I was watching the network feed of the launch, capturing stills from the monitor to our electronic still storage system. I had made a series of captures as the launch progressed to "...Challenger, go at throttle up" then the unexpected fireball occurred. I'd already seen enough launches on TV to know that fireball meant that something was catastrophically wrong wrong wrong and immediately thought to myself "fly out of it... fly out of it... I expected the shuttle to do just that, gloriously emerge from the flames, the crew making a miraculous launch abort and return to launch site... but no. Debris continued on a ballistic trajectory then, its momentum spent, began to rain down while the SRBs traced those heinous arcs in uncontrolled flight. My boss, the station's Art Director was watching with me and asked what happened. I had to tell him it blew up.