Re: At reader level yes
Wrt to the collision rate of fingerprints, that is a side issue. It actually becomes worse in some cases. Some occupations are notorious for using chemical compounds that effectively eat away the prints so for those people the templates have a lot less points of interest and so collisions become possible. Most APIs won't let such people record a template. But the templates are basically a set of angles and distance measurements. No two scans of the same finger would ever result in the same measurements any more than taking two photos from a tripod could create a byte wise identical bitmap. The question is never "are they a match" (hint: infinite FRR). It is always "are they acceptably close". That's where the complex math starts because you are expecting features in a similar location to distort in a similar way, and some features are missing altogether because of sloppy scans.