Not sure it will happen, but I think it could actually be a smart move in a way. Someone correct me if I'm wrong, but i believe Russia doesn't really have any troops west of Kyiv. Imposing a no fly zone over the whole of Ukraine would be fairly big escalation with potentially huge consequences. Simply starting in West Ukraine would be a much smaller escalation as it wouldn't necessarily lead to direct confrontation with Russian troops immediately, hence making it harder for Putin to escalate from there.
Proverbially it would be NATO dipping their toes in the water to test the Russian response, and free up some Ukrainian forces to concentrate on the active war areas. At the same time, if Russia don't have the balls to immediately retaliate, extending the no fly zone to more areas in the country, when half of the country is already one, would seem a smaller escalation than doing it all at once.
Of course it would still be a fairly big step, and Putin probably wouldn't respect the no fly zone over Kyiv for instance. But it probably would give him a headache as to how to react.