I understand the obvious reasons for not doing it, but my honest question is whether that will actually get us anything in the long run.
It will change your Standard of Living, assuming you're an American.
The US is an empire and has been since 1898. Like all empires, it must expand into new markets or the empire will stagnate, and then collapse.
You need only do a cursory review of history to know that is true. Note that the collapse is not sudden, meaning it doesn't happen overnight or over the course of weeks or months, but usually is 2-4 generations.
Perhaps it is best if your own government explains it to you:
The costs of not implementing this strategy are clear. Failure to meet our defense objectives will result in decreasing U.S. global influence, eroding cohesion among allies and partners,
and reduced access to markets that will contribute to a decline in our prosperity and standard of living.
[emphasis mine]
It's called Geo-Political Strategy. Only a few countries have one, because it costs a lot of money and requires a lot of assets and the labor to do it.
Denmark cannot, because it does not have satellites or global aerial recon capability; doesn't have carrier battle groups or amphibious assault groups; doesn't have air power or a large military; doesn't have the intelligence network or even the ability to gather intelligence; and doesn't have the money.
Some countries are capable of a Regional Geo-Political Strategy. India would be one. Brasil is another.
The end-game of US Geo-Political Strategy is for the US and Britain to gain control of the eastern Russian republics and carve it up for themselves, and maybe throw France and Germany a bone.
Russia knows that, which is why they have invaded Ukraine, and that's also why the US bombed Yugoslavia and Libya and bankrolled the Arab Spring and invaded Iraq and Afghanistan and is now involved in Syria.
The US/NATO have successfully driven Russia out of the Mediterranean Sea, save for Syria, in its attempt to pen Russia up in the Black Sea.
For instance, is Putin any more likely to use nukes now if we establish a no-fly zone and or use our air power to help stop his advances, than he is in 6 months when his economy is totally cratered from sanctions and he is surrounded by domestic opposition. Or are we just buying time, simply because "nukes in 6 months" is better than "nukes next week?"
Had you been a NATO observer on Druzba '86 with me tasked with observing Soviet nuclear weapons operations in a field environment, you'd know that Russia's nuclear weapons policy was always no first-use, no escalation and
quid pro quo response.
If you understand that, then you'll understand why Russia's response to the aggressive and hostile US/NATO deployment of Jupiter IRBMs to Italy and Turkey was to deploy SS-4 and SS-5 IRBMs to Cuba, which is erroneously referred to as the Cuban Missile Crisis even though it is more accurate to call it the Kennedy Political Crisis.
That aggressive hostile action by US/NATO allowed the US to target 100s of cities in East Bloc States, including Moscow.
The only way Russia could respond to a Jupiter IRBM attack on Moscow would be to escalate to an ICBM attack on Washington DC, and that was unthinkable, even for the Soviets.
By putting IRBMs in Cuba, Russia negated the US/NATO advantage and restored parity, since the US is not likely to launch a Jupiter and nuke Moscow knowing that Russia can respond in-kind and launch an SS-4 to nuke Washington DC.
While the US withdrew and dismantled it's ERWs --Enhanced Radiation Warheads or as the Media prefers: Neutron Bombs -- the Russians still have ~3,000 neutron warheads consisting of 1 kt artillery fired projectiles (similar to the 1 kt device the US had) and short-range missile warheads in the 5 kt to 12 kt range (similar to the 10 kt Lance neutron warhead) and gravity bombs in the 1 kt to 12 kt range.
Note that it is not possible to build neutron bombs greater than 20 kt.
And if he ultimately succeeds in Ukraine despite early setbacks, will he not just be emboldened to go further?
It is ironic that you mentioned a No-Fly Zone, because the reason the US wants Ukraine as a NATO member-State is so the US can use air bases in Ukraine to enforce a No-Fly Zone over Russia while the US and Britain are carving up eastern Russia.
The only expansionist forces here are US/NATO expansion. Russia just wants a neutral buffer-State, which is something Russia has historically insisted upon having for centuries, so it's not "new."