I like the fact that "fighting the borrow checker" is an idea from the period when the borrowck only understood purely lexical lifetimes. So you have to fight to explain why the thing you wrote, which is obviously correct, is in fact correct.
That's already ancient history by the time I learned Rust in 2021. But, this idea that Rust will mean "fighting the borrow checker" took off anyway even though the actual thing it's about was solved.
Now for many people it really is a significant adjustment to learn Rust if your background is exclusively say, Python, or C, or Javascript. For me it came very naturally and most people will not have that experience. But even if you're a C programmer who has never had most of this [gestures expansively] before you likely are not often "fighting the borrow checker". That diagnostic saying you can't make a pointer via a spurious mutable reference? Not the borrow checker. The warning about failing to use the result of a function? Not the borrow checker.
Now, "In Rust I had to read all the diagnostics to make my software compile" does sound less heroic than "battling with the borrow checker" but if that's really the situation maybe we need to come up with a braver way to express this.