2FA I guess you mean 2 factor authentication? I guess the cost burden is overestimated. India has made it mandatory for all POS and even online transactions to have 2FA, like Visa's 3D secure service for online and ATM pin for POS. Other providers also have it implemented. It must be not very expensive to make the same service in other parts of the world. Wondering why they are not doing it. In India, RBI had released stricter guidelines for that after initial spike in card fraud during the online business boom. Not sure of how much percentage it helped to reduce the fraud, but it's a safe feeling that even if your card is lost or it's details are stolen, you are not robbed of your money in the bank.

[Edit] And if you are wondering how companies can store the creditcard data for automated payments like Uber, they cant .Uber have tied up with payment wallets to make payments seamless or you have option to pay by cash. For business there is an option for interbank automated transfer but that require you explicitly singing agreements.