I specifically meant that the value of NOAA's data and services, each year, well exceeds the annual cost to taxpayers.
Sure it's probably true that overall value of NOAA's services provide more value than the worth of the funds allocated to them. Of course you can't force someone to agree to spend money; even if it's a small amount of money, and the benefit of spending it is obviously worth 1000x the cost -- it is possible that for some reason they choose to disregard that value or that deal and prioritize other things even more. And if they had been persuaded, then the taxpayers would likely not be cutting that budget.
To be pedantic: taxpayers didn't cut the budget, their representatives in Congress did. It is not at all obvious to me that this is what taxpayers want.
The thing is in a representative democracy: Congress speaks for the taxpayers. The actions passed by the House of Representatives are the taxpayers' voice. They vote their duly elected representatives, and confer with their elected representatives from time to time, and the representatives speak on their behalf. That is how the whole system works.
I suspect that if you were to ask taxpayers across the country, and present them with the numbers, the majority would say that NOAA's budget is not actually that large, and that cuts to the premier weather service in the country seems like a bad idea.
The taxpayers delegated their voice in the matter by action of their vote. It is the representatives' job to understand what the taxpayers do not and make the governance decisions. The representatives' collective decision is the taxpayers' decision and word on the matter; even in the case of public disagreements and lack of consensus outside the representative body.
at the moment, Congress appears to be particularly pliant to the whims and demands of the Executive, with a particular animus against science and expertise, even when Congress ought to know how penny-wise-and-pound-foolish it is.
The executive was just chosen specifically by vote of the taxpayers less than a year ago. The things they are choosing are extremely unwise, but it is actually what the taxpayers have chosen and voted for. Generally immediately after the election the executive has a public mandate to do exactly what they campaigned for; it is a decision coming from the taxpayers who had a chance to vet their representatives and might have failed to do so sufficiently before voting them in.