The fact that nuclear weapons are about deterrence means you don't want them to be secret. A secret nuclear weapon's primary use would be a revenge weapon. Or to blow up a city in a surprise attack. Neither of which is particularly "defensive".

There's a reason why we have arms treaties and try to be transparent about our nuclear capabilities. I know it's a movie but Dr. Strangelove is a great example of the thinking behind this.

I get that the point is to keep the balance of power in the favor of the US, but the practical outcome was letting Israel secretly develop a revenge/offensive nuclear bomb. If it got used potentially millions would die, and you can't even make the argument that it acts as a stabilizer via MAD.