This falls into a "if it aint broke, dont fix it" kind of thing. Month and Year Birthdate are fairly low privacy info that everyone remembers and are used to giving out" it gets used for so many different checks because we all have the understanding that we give this info out to businesses that need them, switching to other things that in a vacuum would be a better fit in that one specific category in only a tiny amount just isnt worth the confusion and pushback that changing it would cause.

I think you underestimate how common the most common first and last names are. In an even small city you are likely to see repeats of the most common names.

Interesting. Asking because I work in a hospital (in America tho) and making our patients more comfortable is better for everyone. We do serve a lot of homeless people tho, so for that we would probably still need to ask DoB since we need to verify two identifiers.