Many restaurants that are difficult to book hold back a few tables for last minute walk-ins, investors, friends of the owners, etc. Sort of the opposite of the overbook always airline approach. I know some restaurant owners in SF and that has helped me get tables at some moderately difficult to get times over the years - usually because they are holding something back but none of the Warriors showed up that night.
I totally agree with Textuality. I’ve been lucky enough to eat at some incredibly fine establishments. If you just call them and are polite, or use their system, it’s pretty straightforward. The best one so far in terms of trying to accommodate me - including several cases of phone tag - was 11 Madison Park. The worst in terms of accommodation was French Laundry - they never answer the phone, ever, as far as I can tell. Of course that doesn’t work if you are trying to get a table Right! Now! HEY DON’T YOU KNOW WHO I AM?!?