To give credit to the detractors -- I'm not among them -- the point about nuclear poo-flinging was practically absent from the movie.
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Point taken.
Clarke elaborated on the theme of nuclear proliferation in the novelization.
Bowman, as the 'Star Child', notes the orbital weapon platforms crowding Earth's skies and calmly removes them. As cybernetic feedbacks are mysteriously severed, command and control systems go nuts around the world.
In the 1960s and 70s a number of futurists and military planning types (who're often the same people) expected orbital staged nukes to be common by the 21st century. Thankfully, that didn't happen. Well, not yet, anyway.
Clarke also riffed on the story's nuke threat subtext from time to time (i.e., the threat to civilization and therefore, the super ET's elaborate plans) via satellite from his Sri Lankan home/think tank/fortress of solitude.
.d.