"No fly zone" doesn't have a side effect of escalation, its entire substance is nothing but escalation. I think people have some rose tinted view of no fly zones as some objective neutral declaration, but that's basically an artifact of how they have been used to market what was essentially heavy US involvement in other wars. Instead of saying "no fly zone", saying "US jets should attack Russian jets" makes for a more honest description.
The real humanitarian/strategic answer would be to create a UN-sanctioned peacekeeping zone in the western part of the country, backed up by US/NATO forces. This mirrors the WWII style where as soon as Russia invaded the eastern half of Ukraine, NATO would have invaded the west, but paying respect to our modern notion of borders. That NATO has not done this is likely surprising to Putin, since he's basically operating from the old mindset of fighting a WWII style war complete with an appalling contempt for human life.
> saying "US jets should attack Russian jets" makes for a more honest description.
Saying "US jets will directly attack and destroy Russian SAM missile batteries several hundred kilometers within Russian soil" gets the picture across better.
It's just guessing if things will escalate. But it does seem plausible that providing anti-air weapons is less provocative than enforcing no fly zone with foreign jets.