Here's a thought:

If I was looking to put together a four-person relay team for the Olympics, I would want to see candidates run. I want the fastest runners. But, they don't just run in a straight line sprinting, they need balance and endurance. They need to be able to run around a corner without losing their footing, and maybe run for a whole quarter mile or more. Also, they need to be able to pass a baton to another runner while that runner is running away from them, and within a restricted amount of space. Actually only three runners need to pass a baton. But three runners need to be able to receive a baton while running away from the person that is trying to pass it to them. And in fact, two of the runners need to be able to receive and pass the baton. One needs to be able to start from a kneeling dead-stop at the sound of a gun. They are not all equal players.

Would I ask any of them to run up to and jump over a bar upside down? throw a javelin or discus? run over hurdles? Nope.

You should think about what it is you want from your actors, and audition them to see if they'll give that to you.

I want actors who can memorize and recite lines, without stepping on other's lines, all while moving as they've been directed to move. I want actors who don't mug for the audience to get laughs. I want actors who will sit down and shut up when it's not their turn. I want actors who will show up on time (by which I mean early enough to start on time), who are prepared for the work ahead for that evening's rehearsal. I want actors who can work cooperatively with others, who are not shy, who can bring some creativity, but also do what is appropriate for the story/part/moment, and ultimately what I as the director tell them to do, or not do. And so on.

I don't want actors who are good with improv. The only improv will come when someone goes up and that should never happen.

I've just worked with an actor who after seven weeks of rehearsal announced at the first off-book that he has trouble memorizing lines. I never thought to ask at auditions. I wouldn't think I'd have had to. Next time I will. You can bet.

I may, for my next audition, a week in advance give the actors a side including stage directions from the play, ask them to memorize it, and have them come to the audition prepared to run it off-book with props in hand, and set pieces in the way. Having them stand in front of me and read a piece of paper gives me nothing except what they look like, what they sound like, and if they can project. Even if they manufacture some action, it will most likely be cliche and inappropriate.

I've done the improv, I've done scene-with-numbers-instead-of-words, I've done the sing a song. I'll let you know how this works out.