TLDR: WW3 benefits no one, least of all Ukraine and "if it was good for Vietnam it's good enough here" seems misplaced, to me.
The stakes aren't that high.
Vietnam was waged on Domino Theory which was influential at the time: basically, if Vietnam fell, then SE Asia would fall. This anxiety is what led the US to engage in a long war that was hard to win, saw the US mull over nuclear options a few times and led to severely drawing down US troops level in Western Europe.
At the time, the Warsaw Pact and NATO both were locked in an existential struggle for world dominance, to politically and conventionally annihilate the opposite system if at all possible. Nuclear weapons were a constant reminder to stay out of escalatory situations, such as NATO on Warsaw combat, but otherwise, almost every dirty trick was good enough. The stakes were high enough that skirting nuclear risks was acceptable at times. After all, a gradual nibbling down of NATO allies and neutral countries would make the Warsaw Pact stronger.
Not least because Communism, like it or not, was an ideology that was appealing to many, so it could self-sustain by absorbing new gains.
Contrast Ukraine in 2022. Ukraine deserves its freedom, certainly. Its people deserve to live in peace and freedom and they deserve the join the political clubs that they wish to be part of (even if NATO membership is too provocative to Russia). They don't deserve to be bullied and bombed by their neighbor.
But if Ukraine falls, it will, far from strengthening Russia, merely weaken it by forcing to occupy. The Ukrainian people have seen the results of the Afghanistan and Vietnam wars, they know time would be on their side there as well.
From the West's viewpoint, not necessarily the viewpoint of Ukrainians doing the dying, things need to be kept in context. For example, Wesley Clark (retired NATO chief) on CNN was saying that, if we don't stop Putin now, then we will be fighting Russian in Poland later. Which he then segued into advocating for the no-fly-zone. Given Russia's performance to date in Ukraine, the idea that they could achieve much attacking NATO directly is a fantasy. Even if Russia had performed much better, they just don't have the industrial capacity to challenge NATO past the opening weeks of hostilities. So, yes, this type of talk is a dangerous fantasy of "act now, regardless of the risks, because 1938 Czechoslovakia". There are parallels but Western states have, so far, risen far above Chamberlain's model.
That's what I mean by the stakes not being that high. They don't justify ratcheting up nuclear risks, and especially not for half-assed ideas that would be of little actual benefit.
Also, while we should not be looking for ways to placate Putin, we should also not provide him with ready-made propaganda justifying his actions to the Russian people. Who have all sorts of reasons to gradually turn on him if they don't feel their country is actually threatened and start seeing the downsides of this war.
We ignored Putin's nature for far too long, but let's not build him into a behemoth either. Even if Russia had taken over in a quick surgical strike decapitating the elected Ukrainian government it still has nowhere the same ratio in conventional forces against NATO than it did in the 70s and 80s.
Nor does its ideology of kleptocracy export particularly well. The oligarchs may buy property and spread corruption around but no mass popular movement is going to arise anywhere saying "I know, let's just run our country like Russia does it". Some did with Communism, some do with Fundamentalist Islam, no people will want to consciously emulate the Russian model however (though their elites might).
So we must not make the cure worse than the disease. The long term risk from Russia, using conventional weapons, is low.
However both sides are still full-fledged nuclear powers, so it behooves our leaders to be very, very cautious in what they consider escalatory or not. Jet fighters would not help that much, but they could easily up the ante.
FWIW, ISW's March 19th assessment is that
Ukrainian forces have defeated the initial Russian campaign of this war. That campaign aimed to conduct airborne and mechanized operations to seize Kyiv, Kharkiv, Odesa, and other major Ukrainian cities to force a change of government in Ukraine. That campaign has culminated.
The culmination of the initial Russian campaign is creating conditions of stalemate throughout most of Ukraine. Russian forces are digging in around the periphery of Kyiv and elsewhere, attempting to consolidate political control over areas they currently occupy, resupplying and attempting to reinforce units in static positions, and generally beginning to set conditions to hold in approximately their current forward positions for an indefinite time.
Stalemate will likely be very violent and bloody, especially if it protracts. Stalemate is not armistice or ceasefire. It is a condition in war in which each side conducts offensive operations that do not fundamentally alter the situation. Those operations can be very damaging and cause enormous casualties. The World War I battles of the Somme, Verdun, and Passchendaele were all fought in conditions of stalemate and did not break the stalemate.
Ukraine’s defeat of the initial Russian campaign may therefore set conditions for a devastating protraction of the conflict and a dangerous new period testing the resolve of Ukraine and the West. Continued and expanded Western support to Ukraine will be vital to seeing Ukraine through that new period.
The reason I am citing this is that weapons that have served Ukraine well so far, such as anti tank missiles and man portable surface to air missiles will not be as useful to neutralize entrenched artillery deliberately pounding civilian centers from a distance.
Neither will jet aircraft, not over airspace contested by advanced Russian SAM systems, so let's not over-focus on solutions in search of a problem.
p.s. For what it's worth, the debated Mig 29s are also near useless in this context. Russia would just pound Ukrainian airbases from a distance and the Ukrainians do not have enough pilots or the infrastructure to train them in a timely manner. The bulk of Ukraine's current woes are due to Russian ground forces, such as artillery and missile strikes and the Mig29, being an air-to-air superiority fighter isn't useful there. Yes, every bit can help, but it's like buying a Mustang to go off-roading: missing the point.
p.p.s. to steal a point from Zomvid-21, Vietnam was not Ukraine in another sense as well: Vietnam was far remote from the USA, whereas Ukraine is pretty close to Moscow. This would be more analogous to Russia intervening in a conflict in Canada, Mexico or Cuba. So, whatever the level of Russian duplicity and bullying inherent in the "special military operation", NATO needs to be very careful in delivering mostly defensive weaponry, rather than gear that can menace Russian territory.