My experience has always been that - at least since 9/11 - most states are fairly diligent about checking with other states for suspensions and the like when you first apply for a DL, but after that even if you have a warrant out for an unpaid, minor traffic ticket in one county it typically doesn’t show up in the police database in any other county, even if those counties are both in the same state.
Honestly, I don’t the latter has anything to do with technological limitations, I just don’t think most counties want to be proactive about arresting and detaining people - and filling out reams of paperwork - for a ticket that they don’t stand to make a dime on.
About the garage issue. Arizona requires you to register your car in that state if you use it for work so you could live in (let’s say) Blythe, CA and work in Quartzite, AZ and be required by the MVD to get an AZ licence plate. In fact, according to the AZ state law, if you work in AZ you are considered a legal Resident of that state which I think would be considered unconstitutional if you lived in another state because under the 14th Amendment, can’t you be a Resident of only one state?
Some Canadian provinces have only recently moved to tamper-proof plasticized license with photo since 9/11 and demands for more reliable ID.
I have driven the USA, Itlay, France, Great Britain, Australia and New Zealand with just a Canadian province’s drivers license. Never been pulled over by the cops (lucky me!), but the car rental agencies in all those locations have never challenged the validity of my license, and it’s their insurance at risk if I am not valid.
(If I lend my car to someone and fail to check that they have a valid driver’s license, I would be liable to my insurance company for any damage they did).
OTOH, for ID purposes outside of driving, any rule depends on the situation and the reason for an ID check.