You don’t have to be a fanatic, you just have to care about getting a consistent result. A cup of dry flour can vary in weight by more than 20%, depending on how you scoop it, the humidity, etc. That’s such a large variance that you would see the difference in the result. Bake a cake with 20% more flour than you should and it’s going to be dry.
When flour gets wet, it sticks together to form dough. Dough can have large air pockets in it. Dry flour with a bit of humidity can also form these air pockets, albeit typically on a much smaller scale.
Whether you pack flour down or sift it through a sieve into your measuring cup can make a huge difference in the weight.