Significantly the phrase has military origin
Originating in Somalia in 1993, the modern term “mission creep” became part of official U.S. Army vocabulary a decade later. Field Manual 3-07, Stability Operations and Support Operations (February 2003) acknowledges two types of mission creep. The first occurs when “the unit receives shifting guidance or a change in mission for which the unit is not properly configured or resourced.” Lewis and ClarkIn other words you start with a limited objective but this expands to the point where it is no longer clear. This phrase has also been used to describe non-military matters - financial regulation, for example.
The Dictionary of Military Terms