iRule to return URL/URI doesn't log anything?

Try setting the priority to something low (like 10)

when HTTP_REQUEST priority 10 {
  log local0. "URI = [HTTP::uri]"
  log local0. "URL = [HTTP::path]"
  log local0. "Host = [HTTP::host]"
}

Other irules may be taking actions that make some of your statements invalid, or are preventing the event from triggering.