The only weapons now that would generate much fallout would be cratering devices (ground bursts), which would be aimed at remote military facilities and very long airstrips suitable for bombers. Air bursts would generate much less fallout.
Maybe the masks will serve a useful purpose after all.
The Trident D5 tosses around W88 warheads at 475kt.
That long range missile has big warheads.
And the Russians have big ones too.
I suspect China as well.
Tell that to the Japanese those weak bombs went off at 1850ft above the ground.