I may not be one of the "clever people" but I do agree with your original conclusion. Since you do not have common VLANs on the 2 x links from either B to A or C to A, or C to B, and all are routed VLANs (from what you said), then no STP should be needed.
BUT, since you said that RSTP blocked some links, you must have some VLANs or config other than one is shown in your diagram. If what is in your diagram is all that is present (and none of these links are configured as a LAGs or AEs), STP of any form should not block any of these links.
Big question is when you had RSTP enabled, who was root bridge and what links blocked?