Obviously this isn't legal advice, but it's what defense lawyer friends have suggested if it ever comes up.
I think that popular video about "never talk to cops" mentions something like it too?
I assume if they don't wait, it helps your court case. They could always go with the "probable cause" argument, but again this can help your case if you can prove they didn't have actual cause.
Your threat model is imaginary, if they are robbers posing as cops, they wouldn't knock and wait patiently, they'd just serve you a fake "no knock warrant" (kick open your door and bust in with flash bang grenades).
I'm sorry, this comment is not necessarily a reply to you directly but to the thread in general--are we talking about the real world or some fictional TV show? Genuine question, is this something a "normal" HN reader should be worried about? Is there any evidence of such incidents happening ("kick open your door and bust in with flash bang grenades")?
My understanding is a valid warrant (which as someone else mentioned does not have to be a physical piece of paper) grants them immediate access and they don't have to wait to verify. If you don't open the door, it will be opened for you by battering ram - demanding you open it is more of a courtesy.
Think about it: say someone has a bunch of drugs, you wouldn't want to give them time to start flushing it down the toilet while they call up and verify the warrant is valid. You kick the door in, arrest them, and secure the scene for forensics and evidence collection.
I assumed something along those lines, but I think they have to knock unless there's a no-knock warrant? I just don't expect they'll be amused if you tell them to hang on for a few minutes while you "verify" the warrant.