Like, the main utility of a doctor is in keeping a power role alive, not in trying to maximize the ability to prevent an night kill.
If you're playing as a doctor in a normal game, you're not trying to protect the person you think mafia is most likely to kill. You're trying to protect the person you want to die the least. This is normally a claimed PR that you believe, or someone who's close to IC status, or is an actual IC. Yes, preventing a kill is nice, but I'd argue that keeping PRs alive to do their thing is the #1 priority for doctors.
With that in mind, doctor hunting for scum nightkills is counter-productive. What's the result of killing off doctors, normally? The positive result for scum is that they then have free reign on shooting PRs! The goal of shooting a doctor is to be able to shoot that cop on the next day. Now, in this game, that's impossible, since there's 4-5 more doctors out there. So, you'll never be able to clear the field of doctors, or if you do, it will take so long that you'll never be able to take time to shoot at the cops, who are the real threat to scum.
Scum are not afraid of doctors guessing the scum. Scum are afraid of getting investigated by a cop. They want to kill those cops.
Scum WILL shoot for cops, not for doctors. Therefore, doctor claiming is awful, and narrows down the pool of who scum will shoot. And trust me, scum figured this out pregame, they are not learning anything new from this post.