They currently have ~4.
There's a reason Russia invests so much in SAM systems. They expect NATO to have air superiority.
Which EW systems are you talking about?
As is, they were able to move into Ukraine without nuclear risk, because the US explicitly said we wouldn't put troops there.
And let's not pretend Russia shooting down a US plane or vice versus would start a nuclear war. It happened fairly commonly during the Cold War, quietly.
What you're describing is reckless brinksmanship. One mistake or misread and the world ends.
"Reckless brinkmanship" is an odd phrase, when we're talking about responses to Russia invading a sovereign country.
So what if NATO puts some forces in Ukraine, but Putin calls their bluff and attacks anyway? Small contingent wouldn't be nearly enough to hold the territory, so you need to either engage for real (but you don't have political capital for that), or withdraw forces which would look like huge humiliation.
This is much less relevant for a constitutional democracy than for a dictatorship.
This is not the cold war, I don't think anyone can predict what Putin will do if provoked and he needs to save face.
NATO is not prepared or willing to start a war with Russia.
It seems that many in the West think they have unlimited power to do anything and interfere in any conflict. Reality is those days are over now.
And hence declaring it before Russia invaded. Which forces Russia to choose to shoot down NATO aircraft, or operate outside those zones.