That is a good idea for one of the pages in the root of the site since a tool and resources to test/improve your site speed should be of interest to my visitors. A problem with hosting a tool to do this is bandwidth consumption since you need to load all of the content of a page such as images. Or if I was clever, I would do it via an application on my computer, analyse the site, and email the subscriber the report. :D Then my unlimited broadband takes the b/w hits.
If it was my site, I would probably optimize for the term "site speed test".