1- The purpose of iddah is not the identification of pregnancy. Pregnancy can be identified today with such easy tests that do not even require a medical doctor.
2- The purpose of iddah (Allah knows the best) is to protect women by:
a) Preventing men to divorce their wives with snap decisions in times of argument and anger.
b) Preventing men to suddenly leave their wives helpless by throwing them out of the home with nothing in their hands.
c) Giving some time for couples to talk through their issues, not letting them to separate right away in times of trouble.
d) Compelling couples to live together for a certain time before divorce as to create chances for them to sleep with each other again and melting the ice.
e) Protecting the family and the children.
f) Giving a lesson to all managers (qawwam) that they cannot just fire their employee at will without giving them some time (notice period) to prepare themselves mentally and economically as the husbands are named Qawwam (manager and protector) in Quran (see 4:34).
Divorce is a difficult process. It is always more difficult for women than men. Allah entitled women as “muhsana” in Quran which means “the protected”. Therefore, Allah always protects women in their affairs. Iddah is just one element.