I am pretty sure the short answer is no, but I have wondered about that too. A concrete way of asking that question might be this:
Is there anybody on the Forum that has no store cards of any kind, open or closed, and who neverthless has achieved a score above (say) 845?
Thom Thumb (with an 850) posts here a lot. I wonder whether he has any score cards.
If I understand it right, the CRAs certainly give scoring models the ability to do that, in terms of giving accounts types and subtypes. Thus a scoring model can see that a mortgage loan, a student loan, and an auto loan are all of the Installment type, but can also see that they are of those subtypes as well. Thus a model can in principal give you extra points in the credit mix category for having mutliple subtypes of installment loans.
Similarly it's theoretically possible for a model to give you points for having two different subtypes of revolving accounts.
But does it? That's your question. I personally don't know. For what it is worth I have obtained very high scores (844) with no store cards and a profile that is imperfect and some known ways, so if I am losing any points it must be only 1. As a practical matter therefore I personally think one should only add a store card if you really see a massive advantage for that particular card -- e.g. if you see that you will be buy an enormous amount of stuff at Target over the next 10 years, then sure get the 5% cash back card (better than using your Citi Double Cash).
