I think you are right, and this does seem to be an oversight. I don't know about other browsers, but with Firefox you can search whatever page you are looking at by clicking "edit" at the very top left menu bar, and then clicking "find', and then typing in your search term. Of course, you would have to repeat for each page of a multi-page thread, but at least the "find" window stays open and the last search entered remains entered. I assume most other browsers besides Firefox have a similar "find" function.