[sbdaman]

Given it's set to generate random pages on the site, is there even any possible explanation for this that isn't sketchy?

[mediumdeviation]

It's not random, setting the query string to a new value on every fetch is a cache busting technique - it's trying to prevent the browser from caching the page, presumably to increase bandwidth usage.

[gertop]

It's trying to prevent the server from caching the search. Thousands of different searches will cause high CPU load and the WordPress might decide to suspend the blog.