Flour is always the canonical example and I flat out reject it. It's not true. If you think it's true, you've convinced yourself it's true to avoid addressing other problems in process you have.
Here's a thing: a given measure of flour (by any means, volume or weight), a single one kept in a cupboard, not remeasured, is going to have a different weight on different days that have different ambient humidity levels.
The tools of the kitchen are imprecise. The environment is not well controlled. And human taste is robust against micro variations.
Flour absolutely matters. Some flours are very “thirsty.” Having thirsty flour and compressing it during measurement makes for way too dry cookies, pancakes, etc. We’ve experienced this multiple times in our house.
I started out baking measuring by volume, and it's not like it doesn't work. You can make amazing things basically measuring by handful, pinch, and feel. I think technique and ratio are more important than careful measurements.
Everything else is optimizing for consistency, which might not be important to everyone. If you care about it, measuring by weight is more accurate. The undesirable variations aren't usually taste, but structure and texture, which can be noticeable.
A given weight of flour will have a different weight on a different day?
As it absorbs more or less moisture from the air due to ambient humidity changes, yes. The same reason your wooden furniture will also significantly change in dimensions such that there's no point in being more than 1/16th of an inch precise in your measurements; your design and construction technique is far more important.