Without the fanfare it might have been done.
My suspicion is that the fighters were too big an item. The NATO thinking is probably that this will devolve into a guerilla war, like Afghanistan in the 80s: The Russians eventually overrun the cities and install their puppet government. The play is to provide man-portable weapons, like Stingers, Javelins, and, iirc, someone is sending Carl Gustaf recoilless rifles, so the Ukrainians make the Russians bleed, a lot, for years.
The more I think about NATO deploying “peace keepers” in Ukraine, the more I wonder why that wasn’t done a few weeks ago. The threat from Russia was clear. NATO has deployed outside of NATO member states before.
NATO in Kosovo
Today, approximately 3,500 Allied and partner troops operate in Kosovo as part of NATO’s Kosovo Force (KFOR).
NATO in Afghanistan
…the International Security Assistance Force (ISAF) was established under the request of the Afghan authorities and a UN mandate in 2001. ISAF was led by NATO from August 2003 to December 2014
NATO and Libya
-the enforcement of an arms embargo on the high seas of the Mediterranean to prevent the transfer of arms, related material and mercenaries to Libya;
-the enforcement of a no-fly-zone in order to prevent any aircraft from bombing civilian targets; and
-air and naval strikes against those military forces involved in attacks or threats to attack Libyan civilians and civilian-populated areas.
https://www.nato.int/cps/en/natolive/topics_52060.htm
Why did NATO wait until after the invasion started to mobilize the Rapid Response Force? Probably because the bad actor was Russia, rather than Libya, Afghanistan or Serbia.
Steve