Big-O is just a formal notation for comparing growth rates of functions. You are right of course, that often one might get away without the precise formalism an

Big-O is just a formal notation for comparing growth rates of functions. You are right of course, that often one might get away without the precise formalism and rely only on a gut feeling - but there are limitations on how many things we can compare mentally. A bit tongue in cheek one could make the following analogous statement: does anyone use greater-than or less-than or equals signs at work, as in something being "> 5" or "< 10"? In my experience "this quantity is much larger than that other quantity" or "these two quantities are roughly the same" is perfectly fine.