I've thought about claiming more.
Let's say that the Doc claims today. Those of us who are town, and not the Doc, now have a 2/5 chance of lynching scum (this gets better based on our reads). Gives us decent odds of lynching scum today. If we lynch scum today, everything is fine and dandy.
But what if we lynch another VT? Scum then is faced with the choice of either killing the Doc or hunting for the Cop. Let's say they kill the doc.
D3 will dawn with 5 players left. 2 are scum, 1 is the Cop, and 2 are VTs. The Cop will have a result on someone - if it's scum, we will have a choice to make. Because it is LyLo (lynch wrong and lose), scum will also claim to be the Cop and have a result on someone. The good news is that in this worst-case scenario, we have a 50/50 chance (improved by our reads). That's not too bad.
What if scum got lucky and killed the Cop? Then D3 is 2 scum, 1 doc, 2 VTs. But the doc is actually an IC (known town) so we can't mislynch him, and scum don't have the opportunity to fakeclaim doc (because the doc claimed today, D2). The VTs have 2/3 odds of lynching scum. And the doc has a chance of stopping the kill at night (only if we get it right, if we don't then that's an endgame scenario because eventually the doc won't get it right and scum have a majority of town).
These are the scenarios where we mislynch today and the doc has claimed. I think they're both pretty good.
What if the doc doesn't claim and we mislynch today? If a VT dies overnight, 5 players left, 1 cop 1 doc 1 VT 2 scum. Scum will totally fakeclaim a PR. 50/50 odds again.
If they kill the cop, D3 is 2 VTs 1 doc 2 scum. Scum fakeclaim (probably). 50/50 odds?
If they kill the doc, D3 is 2 VTs 1 cop 2 scum. Scum fakeclaim because they have to because the cop has results.
So actually I'm ambivalent on if the doc claims but I lean yes. What I haven't commented on yet is that we will have the benefit of an IC doc for the rest of today, plus their interactions on D1 to re-read and know.
So, doc should exercise their own judgement on claiming today. It might be a good idea. At worst, it is an indifferent idea.