If you don't have the ability to produce tritium then every twelve years your arsenal halves in size as you cannibalize your arsenal to supply your arsenal. Russia may have gone through four generations of this cycle. And that assumes they're managing the situation competently.
Deuterium and tritium are used for fusion, that is, for strategic thermonuclear bombs. Thermonuclear bombs make up a small percentage of every nuclear arsenal in the world. Tritium can be made from deuterium. In 2003, Iran and Russia built a reactor to obtain deuterium in Iran. To no avail!
Cesium is used as a trigger in nuclear warheads. That boost is relative and in most cases small tactical nuclear warheads are aimed for, not for boosted.
Most of our warheads are not small tactical nuclear warheads. And you were wrong about the tritium. It is used for fission bombs.