Is there a specific term (name of a "metric") that represents the growing level of unstructuredness (or just plain badness) of a s/w component that is caused by too many changes, by too many people, over too long a time interval?
Technical debt is a recent metaphor referring to the eventual consequences of poor system design, software architecture or software development within a codebase. The debt can be thought of as work that needs to be done before a particular job can be considered complete or proper. If the debt is not repaid, then it will keep on accumulating interest, making it hard to implement changes later on.
But it seems to refer more to bad changes instead of many changes.
I have three suggestions:
Entropy (but in its physical meaning and not in its information science meaning) As wikipedia says, the term entropy is often used to describe the "measure of disorder of a system". I think the situation you described could also be interpreted as the growing disorder of a software system.
Architectural drift which describes that your software architecture is slowly drifting away from the original idea and gets more and more chaotic since new architecture decision are not adjusted to existing ones.
Software Erosion Like the geological term this describes that the structure of the whole software systems breaks more and more apart because new features or bug fixes are not integrated well to the system. And beginning from the edges, the whole architecture looses its shape.