Is there a commonly used term to describe the organisational phenomena whereby procedures and processes become increasingly complicated and arduous?
Excessive complexity in processes is called "Red Tape"
You can see the Merriam Webster definition of red tape here: Official routine or procedure marked by excessive complexity which results in delay or inaction.
The term originates from the red tape formerly used to bind legal documents in England.
You can see the Wikipedia definition of red tape here: Red tape is an idiom that refers to excessive regulation or rigid conformity to formal rules that is considered redundant or bureaucratic and hinders or prevents action or decision-making. It is usually applied to governments, corporations, and other large organizations.
Tendency to manage an organization by adding more controls, adherence to rigid procedures, and attention to every detail for its own sake.
Red tape is about right, but it refers to the outcome not the process. I found Bureaucratization here. This is the correct meaning but the word is a mouthful and certainly not commonly used.
I think it's just called waste. I never heard of a specific term other than waste being used. Look for TIM WOODS in your organization:
T: Transport I: Inventory M: Motion W: Waiting O: Over producing O: Over processing D: Defects S: Skills
These are the eight areas where you can lean your process.