I remember my dad used to talk about such devices. In my day (my heyday), it was the nuetron bomb that caused a stir. Although it was not intended for such longlasting radioactive effects. It was more intended to even the 'playing field' of Western Europe. In the 70s (in my military days), we used to war game against the Soviets expecting a single US brigade to have to go up against 3 armored Warsaw Pact divisions. Everyone quietly expected it to go nuclear within days, if not sooner - if it ever happened.
I have a book written during the era "Soviet Military Strategy" - and the scenario was at least a 3 to 1 Russian advantage in ground forces which WOULD only have been stoppable with tactical nuclear weapons. Western strategy was to try to build tanks that were 3 times better than the Warsaw Pact 3x advantage in numbers - but nobody really believed they could stop the East conventionally.
The Soviets, on the other hand, were pretty certain to have been planning the use of their own tactical nukes ahead of their attack to open up the lines.
Nobody could figure out if such a scenario could have been played out without one side or the other resorting to the big ICBMs - i.e. New York/Moscow.
BTW - what the heck was a "Cobalt Bomb" supposed to be in On The Beach?