Word meaning 'a system of unnecessary rules'

Solution 1:

Bureaucracy

: a large group of people who are involved in running a government but who are not elected : a system of government or business that has many complicated rules and ways of doing things (m-w.com)

Micromanagement

: to try to control or manage all the small parts of (something, such as an activity) in a way that is usually not wanted or that causes problems (m-w.com)

And finally, an allusion that really sums it up: "On Wednesdays, we wear pink."

Solution 2:

There is an idiom called Red tape that is closely related:

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.

Examples and a definition from the book "Idioms in the News - 1,000 Phrases, Real Examples" By Peter Bengelsdorf: