I mean, they don't have to be. You can often get a state ID card and a driver's license, but that's essentially redundant. More fees, more time, more paperwork. Things that require an ID just require some state or federally issued photo ID, so you can use a DL, a state ID, a passport, etc. When the extreme majority of adults are already needing a DL to get groceries why bother with another ID.
I wasn't able to find any states where this is the case. They all appear to have rules that say you can only be issued a state ID or a state drivers license but not both at the same time. Additionally federal REAL ID rules have the same requirement for REAL ID compliant identification.
