You have to view the issue from the relevant perspective. In 1945, the idea was for the allies to share administration and policing within their relevant area, but while Allies it wasn't expected that these areas would become borders nor that travel between sectors would be prevented.

That stopped with the Berlin Airlift of 1949, precipitated by the USSR closing the roads and links to West Berlin. Since this was always regarded by the West as an illegitimate action, Berlin was regarded as having been placed under siege. In 1960 formal barriers were built, and the siege state had a tangible physial manifestation.

Because the Soviets built the barriers, Berlin was regarded as a city under siege. Had NATO built the barriers as defences, then it might have been regarded as an enclave.