Joining a program like NEXUS or Global Entry is the only time I’ve had my fingerprints taken by the govt. When I worked for a couple highly-regulated financial institutions I was fingerprinted as part of a background check but that was done by a private party who (allegedly) was just checking for matches with known criminals.
AFAIK only if you are booked into jail, and also for some licenses. For example, a beer and wine license for a restaurant requires fingerprints, at least in my state, not sure how it varies. Probably some types of firearm licenses as well. Not typical driver's licenses though.
Truck drivers and substitute schoolteachers too (I was a sub teacher at one point and the closest place to go to get fingerprinted was a truck driving school.)
joined the military. they did fingerprints and IIRC they were starting to log DNA.
if you have access to profoundly expensive weaponry and training to use it, it makes sense. also if you're shipping bodies back in pieces -- fingerprints, dental records, and DNA may be the only way to figure out what happened to you.