You click the Start Button to stop your computer for the same reason you turn your ignition to stop your car.
One of the things I studied in computer science was "useability." How to make programs intuitive to use. So, yes, you click START to start the shutdown process, as it were.
By the way, for those of you who have been around for a while, you'll note that useability is an elective most programmers don't take. It's pretty obvious in the design of many programs.
For further reading:
https://devblogs.microsoft.com/oldnewthing/20030722-00/?p=43083James