If you need it, then you need it. Most people (including professional vol traders don’t.)
If your example took days for you to figure out then formalizing the second order Greeks isn’t your solution. It’s an intuitive understanding of how options work. you learned something in that analysis. Next time you will be thoughtful about this risk factor when you put on a similar trade. And next time you will encounter another risk factor that will take days for you to understand. That’s how the learning works.
I’m learning everyday and I’ve been trading vol for almost 20 years. I bet @sle will say the same thing (and he knows a lot more about vol trading than I).
Especially for those who are math and computer challenged, it is important to live on intuition. That is how I survived trading options for the last 6 years now going 7.

