As often as not, a well-cut sport coat and trousers play as higher status than a suit. It explicitly signals that you're dressing well by choice rather than diktat. Many semi-formal flourishes can carry this connotation - brown dress shoes, a knit tie, an oxford shirt or a flamboyant pocket square.
There's some historical precedence there. Up until ~10-15 years ago the fakers and know-nothings used to always wear suits. They were the guys who pulled the purse strings, but had no clue.
Unfortunately, since then they've learnt to mimic the dress of their prey. So now instead of the "empty suit" you have an "empty hoodie".
But the problem with a very strict dress code is that you don't feel being respected, you feel coerced.
When I was younger, I chafed. Now, I enjoy getting seated at that restaurant table before you.
It's just an observation that the more professional you look, the better you'll be treated. Yes, that's a fact. Yes, it's probably a sad commentary. And I rarely wear dress clothes - but I know when to, and I don't complain.
Anecdotally, I have worked at restaurants where we wouldn't seat people who were wearing denim, no matter how expensive it was.