Unless you're actually writing complex tools - no, you're probably not getting a "formalized way of modeling" what happens to your program.
If somebody tells me "hey, I have to keep manually testing this and that, I'm losing a lot of time, how about I spend 2 days writing my test thing?" - I'll say Sure!
But if someone tries to convince me in the abstract - I'll be skeptical. Developer busy-work is real.