NWS is important but not everything NOAA does is absolutely needed. Unfortunately, the administrators of NOAA have had the ability to apply the scalpel approach on their own to reduce expense for decades, but chose not to, and thus have now incurred the outside axe approach.
I didn't vote for Trump, but I have for decades watched the inevitable expansion of government bloat and waste of taxpayer funds.
Unlike the private sector where the "nice to have" but unnecessary tasks are eliminated with 10 percent reductions every recession, government never goes through that as its managers always tend to increase staff and budget so they can qualify for the better pay of a higher GS level. So this initiative is long overdue.
Look up "Parkinson's Law" which I studied as an undergrad to understand why such budget creep inevitably occurs
https://en.wikipedia.org/wiki/Parkinson%27s_lawAnd then study the "Washington Monument Syndrome" for why cuts are always at the local offices instead of the Department of Commerce Executive offices:
https://en.wikipedia.org/wiki/Washington_Monument_syndrome