Attacker can record encrypted data before getting the masterkey. During usage, all pieces of master key will have to be brought together into one place (phisic

Attacker can record encrypted data before getting the masterkey. During usage, all pieces of master key will have to be brought together into one place (phisical or virtual), so eventually still only one breach is needed. If I encypt data using encryption without backdoor, then to illegitimately get clear text requires effort X, and it gives access to 1 persons data. If whole country encrypts data using backdoored scheme, then effort Y will give access to data of 100 000 000 people. It would seem that security of the backdoor should be 100mil times stronger then that of usual crypto.