I have not entered Belize since they started this, but the other countries I have visited scan both on entry and exit.
Again, I don't think "crazy" is an accurate adjective to describe the technology. Documents can be altered and immigration officers can be lied to. Finger prints are difficult to alter and don't lie.
Flip side of this is it can be a convenience to legally traveling individuals. The US Global Entry System is a good example. Having been prescreened and fingerprinted, when I enter the US I go to a kiosk, scan my fingerprints and breeze thru immigration not having to stand in line waiting to be interviewed by an immigration officer.
I can easily make a connecting flight within an hours time.