There are more reasons, and it goes a lot deeper, than just following this one pattern. The entire binomial theorem relies on 0! being 1, unless you start putting in huge numbers of exceptions and special cases.

Here's a better answer: https://mathforum.org/library/drmath/view/57128.html

If you prefer video: https://www.youtube.com/watch?v=Mfk_L4Nx2ZI

The title should be "Why 0! = 1!".

had a typo. My intended title was 0! = 1