Farci, If the UK was part of Schengen you likely would not have had this problem, as there would not have been any arrival controls. (Although the waiver of the 3 month validity rule is only valid for citizens of the EU/EFTA countries). The only time my non-EU passport is looked at is when I fly to/from a non-Schengen country.
The data is for transmission to the governments, and data protection laws limit how airlines can use it. (They cannot even keep it in their systems for future trips without your specific agreement). Of course every country's laws are different - the US doesn't care, the EU cares deeply). The requirements of each governments requirement are very (as in very, very) complex and cannot really be encoded into a system that can be checked against. For example some countries visa-free period varies based on the purpose of the trip (business vs. pleasure).
It would certainly be nice if governments used the data sent to them as a 'pre-check' to expedite the actual arrival process but many (most, all, ??) do not.
My wife and I have different passports. I always check when travelling to a new country. For example, who would have thought that Northern Cyprus' immigration is governed by Turkish rules (which require a 6 month validity for non-EU nationals).