This gets thrown around a lot, but has two major problems. First, it's unlikely that comparable funding will also be transferred from NASA to NOAA. E.g. NASA will be told to stop earth science research and have it's budget cut appropriately. NOAA will be told to start earth science research, but without the requisite budget increase. So effectively, it kills earth science under the guise of "moving" it.

Second, NOAA is not operationally or logistically equipped to handle the level of earth science that NASA is performing. NOAA manages a few weather satellites, but has nowhere near the infrastructure that NASA has, and requires, to manage the existing earth science research. Even if you gave NOAA the appropriate money, they don't have the infra or engineers to keep everything flying.

Planetary Radio did a great episode on this topic, but I'm struggling to find it right now.