Why theory at all
A case interview is not a maths test. It is a test of whether you can decide something sensible with incomplete information, out loud, in fifteen minutes.
Arithmetic gets you to a number; theory tells you which number to compute and what it means once you have it. Every framework here exists because it answers a recurring question: is this business earning more than its capital costs, is this difference real or noise, is this advantage defensible. Learn the question each tool answers and the tool becomes hard to forget.