The T in FIRST didn't mean Thorough originally. The T was for Timely.
There's a post by Tim Ottinger on his blog "Tim Ottinger's thoughts on Software Development" that explains the history of the FIRST acronym:
FIRST: an idea that ran away from home
Google it because it seems that as a new users I can't add inks in comments.
I agree with you. I think that I, R and S can be applied to other type of tests other than unit-tests.
I liked your post. Thank you!