That sounds weird. Which country abuses passports like that?
From my perspective, a passport is just an identity document. It's not a source of identity. When you get a new passport, your identity doesn't change, so you don't have to update your information anywhere. Immigration officials may be the main exception, if you live outside the country of your citizenship. Or maybe there is some hassle if you need to transfer a visa to the new passport.
Lots of countries use ID's serial number as a sort of identity. Like, your bank would literally store "Mr. John Doe, G.I. ID 60-05 123-456-9012, D.o.B. 1985-07-29, etc." in your record, and when the next time you visit a branch and show them your new ID, it better have a "previously issued IDs" section on it with that old ID number there, so they would confirm that it's still you and update their record.
From my perspective, a passport is just an identity document. It's not a source of identity. When you get a new passport, your identity doesn't change, so you don't have to update your information anywhere. Immigration officials may be the main exception, if you live outside the country of your citizenship. Or maybe there is some hassle if you need to transfer a visa to the new passport.