I wouldn't use the word "cheap," but it doesn't look all that unreasonable, given what we're dealing with here.
But, to the extent that the bean counters can, somehow, draw a bunch of arbitrary lines in the sand and directly attribute some 11% of the US military budget to the nukes keeping the peace on behalf of the entire Western world, it doesn't appear excessive.
At some point there may be a phase change where the US abandons this goal. In that world, the rational strategy becomes one of strategic disengagement, so that if nuclear war breaks out (or a conventional war that risks going nuclear) the US is not drawn in. The lesson becomes that of WW1, not WW2.
So say you. This is a discussion about costs, as opposed "goals." Were I to stipulate the claim you make, then it's all be a terrible failure: at least three US allies have built and currently operate a nuclear arsenal.
That’s probably a good thing; certainly the people complaining here about costs would not suggest we go back to doing so.
Similarly, part of the reason the UK has repeatedly decided to retain its remaining nuclear weapons (Trident submarines) is that nukes were and are, pound for pound, very inexpensive compared to other weapons.