Believe it or not I don't think that is even close to being the case.
A quick search found that an Arleigh Burke-class DDG has ~24 officers and 300 enlisted and a VFA squadron has ~20 or more officers, depending on if it is an E or F squadron, and ~200 or so enlisted personnel. Add up the all carrier, maritime patrol/recon and helo air wings (whose squadrons usually have A LOT more aviators than VFA) along with the large training wings as well (that SWO's don't have) and you get quite a few officers.
From looking at the November 2021 Officer Inventory Authorization, there were 9,175 SWOs and 12,687 in Aviation (no breakdown between pilot and NFO). There were a total of 27,361 URL officers, 7,459 RL officers, 10,420 Medical Community officers (and a total of 15,666 among all of the Staff Corps), and 5,437 LDO-CWO types, for a total of just shy of 56,000 total officers.