That one's easy: wiretapping is painted as an evil commie thing (in fact it's widely seen as the second key reason why the eastern system was bad, lead closely by shooting people at the wall and followed at great distance by smaller cars), while IDs were as real in the west as they were in the east. Also, while people in the east had real problems with a wiretapping organization completely out of control, them not having IDs would have hardly made any difference. One could easily argue that making a difference between those two things is based on some solid experience and therefore isn't odd at all.

Both german states were running like virtualized OS instances hosted by occupation. Under those conditions one would probably give an ID-less system about as little consideration as a liberal reimplementation of the second amendment. When that changed nobody felt much like messing with the proven western system envied so much by those in the east.