It would be constitutional if they had the votes but they don’t have the votes. If they had the votes they could force a nominee of their liking, or else keep an “Acting Director” indefinitely.... but they don’t have the votes. So long as the Republicans can stick together, the Demoncraps can’t do more than rant at the new nominee in the confirmation hearings. They can do procedural delays and even filibuster, but McConnell and co. can ram the new nominee through... they just need to grow spines. But they did ok with Gorsuch!
That’s what I was driving at. :-)