Easy to say from our relative positions, but would you really take that gamble if it was your call to send NATO troops into Ukraine?
Risking nuclear war isn't worth it. Besides, we've war gamed a huge variety of possible outcomes to this (and have been doing so for 20+ years), if NATO intervention looked like the correct path, we'd take it.
Sometimes I think civilians think these decisions are a coin flip, but strategists, commanders and intelligence agencies have been planning this across multiple administrations for decades. This was a known flash point.
I think you might be overestimating how clear the line strategists have on this conflict is. There are many diverging opinions among security experts, and current/ex strategists on the correct course of action. Those in the realist school of political thought think capitulating to Putin's security interests and finding a way to mutually de-escalate is the right approach. While many others think a relentless push by the West to punish, isolate and degrade Russia economically, politically and militarily is the best approach.
Either way, avoiding nuclear escalation is a crucial consideration. What's weird to me is that the West has yet to draw an ethical line indicating what might trigger more direct involvement. The strategy at this point seems to be a slow burn of Russia's military capabilities, which considering he has tactical nukes, seems risky.