In The Witness, are there puzzles that DON'T do anything?

Solution 1:

For what I remember, the "room with coloured light puzzles" in town centre lets you solve some Environmental puzzles. Which are not mandatory.

Those triangle puzzles are called Discarded panels, you need them to learn how to solve that kind of puzzle for future use:

These panels seemingly serve no purpose, are often hidden or out of view, and do not appear to be connected to anything. However, they can be "solved," even if they don't open any doors. The solutions aren't random and actually teach you an important concept for the end of the game.

Regarding the Quarry, some puzzles turns on devices: an elevator outside and a control panel for a small lift. Other puzzles let you unlock the metal latches blocking the panel to activate the Quarry laser.

But if you mean this one, located inside the control room:

it apparently does nothing, it has the only purpose to teach you

that the symbol can eliminate any rule from the board.

So yes, there are several "useless" puzzles scattered around, you may want to complete them just for completion.