Once one country starts making nukes you cant stop everyone from following suit to protect themselves.
Except we did stop. We ended nuclear testing. We downsized our arsenal. We never deployed the high yield, neutron bombs, or other "tactical" variants in subsequent wars. And neither did the French or the Russians or the Chinese. Or even the Israelis.
Our nuclear program is derelict. It belongs in a museum. There's an outstanding question as to how many of the bombs currently in circulation are duds.
Unlike with the F-35 or the Bradley Fighting Vehicle or the Predator Drone or even the Virginia class submarine, we're just not putting any more money into nuclear proliferation and improved first strike capabilities like we were 60 years ago.