What you describe there is "make absolutely 100% certain that the territorial integrity of Ukraine will forever be destroyed", which is kinda the precise and exact opposite of "help preserve the territorial integrity of Ukraine".
Protecting the western part of Ukraine doesn't mean renouncing its eastern and southern parts.
It seems to me that, if NATO could have the courage to send troops in the western regions of Ukraine, after a request by the legitimate government, at least, refugees would have somewhere to go, and the Ukrainians would no longer be so desperate.
In 1939, the U.K. and France declared war on Germany because of the invasion of Poland, which was, in my opinion, a terribly counter-productive move (no details here) and an overreaction.
In this situation, when we have a country (Russia) with dictatorial tendencies which attacks its western neighbor, using mostly fake reasons for justification, it is not desirable to declare war on Russia (good that NATO doesn't do it), and NATO is right to not impose a no-fly zone over Ukraine (Zelensky requests it, but this would involve shooting down Russian planes right away and would be very dangerous; in addition, it's not really up to NATO to decide who may or may not fly over Ukraine).
But, there is, in my opinion, much more that NATO can do to help Ukraine, in addition to sending mostly light weapons, which include Stinger anti-aircraft and Javelin anti-tank missiles.
NATO could send quickly a large number of armed drones, used by the U.S. military, warplanes (and provide training for Ukrainian pilots), and send a protection ground force in the west of Ukraine.
On the political side, Ukraine could also renounce Crimea, and the two independent republics of Donbass.
Everyone is baffled as to why Ukraine has not done more to attack the Russian convoy as it is a sitting duck for drone and airstrikes.
There are several possible explanations, Ukraine may be running out of armed drones and its small, outnumbered air force may be wary of being shot down by Russian air defence batteries.
Ben Barry from the International Institute for Strategic Studies (IISS) suggests the Ukrainians may well be safeguarding what resources they do have in readiness to counter-attack when the Russians get closer to Kyiv.
(
https://www.bbc.com/news/world-60617145).