It's ironic I have to say. The "sticky" CSS property should only be used for table headers. Yet it is never used anywhere for tables, but instead misused on almost every website for navigation and clutter.
I'm sure there are other good use cases. The fact that almost every site out there makes a point of using it on the worst possible way doesn't justify the "should only be used for table headers", even though, yeah, your sentiment is correct.
I think the step forward is to let website navigation become part of the browser chrome. There's space for a menu item for the website, or a dedicated button.
Maybe even on-site search could become part of the browser chrome?
This kind of integration would also be an improvement for web apps.