Google is going to be including page speed in mobile search ranking soon, so if you've been ignoring your page speed scores, it's probably time to take a look.
In order to test our own site speed stats, I made a little tool that crawls our sitemaps (and sitemap indicies) and runs the Google Pagespeed tests on the pages it finds. Or it can crawl a robots.txt to find out what sitemaps need reading.
I did some searching around before writing the program for myself, and was surprised to see that most of the work so far is limited to developer-oriented scripts where you have to list all of the pages you want to check yourself.
Would anyone be interested in a desktop tool to do this? Basically you give the program a sitemap/robots.txt to start crawling, and it will run the pagespeed tests (mobile and/or desktop) for you on everything referenced.
I'm also debating making a web service for people to sign up for automated checking and periodic pagespeed reports.
If you're interested in trying out our desktop tool for automated Google Pagespeed reports, let me know by sending us an email. Or leave us a comment if you have thoughts! I'd love to know if this is a popular idea, and I'll get the program up on our website.