I like the thinking outside of the box, but this is a terrible idea. First, and probably most importantly, it would reduce the time for the betting people to make odds, and I think sports betting matters in this world. Second, it would reduce the time for sports pundits to analyze and game the draws. Most importantly for me, it would not allow US on forums like this to game the draws, or to play the draw challenges, which you may know I am a fan of, and I will push you to join ours.
Maybe what matters most, though, is that it rarely happens, in a Major, that a player withdraws after the draw is made, or specifically a high-profile one. I would not advocate for this kind of a change just because Novak is going around refusing to be vaccinated against Covid. This, too, shall pass.