Playing chicken is always risky.

Declaring a no fly zone would have achieved nothing. Sending air forces to enforce it would have done something. But what happens if American fighter jets engage Russians over Ukraine, while Russian air defenses support their air forces from their side of the border? Would Americans let Russians launch SAMs with impunity, or would they invade Russia, showing the world that Putin's justification for the war was in fact correct?

Maybe Putin would have chickened out when American jets show up, but you can't know that for sure. Which means you should probably decide in advance you far you are willing to escalate before you chicken out yourself.