Or corporate websites where something as simple as looking at my schedule has a “query run” time

Compared to GGP's approach of having a human do it, this is still fast.

Also not sure why you'd want to share a link to a page where all the images and links are broken in the first place.

Should be O(n) unless you're trying to optimize for every single permutation of query param, right? I'd assume the majority of the time the individual params would be independent from one another. Plus you'd only need to do it once in a while for any given base url and persist the result.