Clarification: "PageSpeed Service" is similar to mod_pagespeed: it accelerates web-pages via the PageSpeed Optimization Libraries running as a proxy in Google's cloud.
You are talking about "PageSpeed Insights" which analyzes web pages & makes recommendations to improve speed. There are many trade-offs that impact the speed of a web page. Etags on HTML improves experience for end-users that come back to the same page. But we also get value from making optimizations that preclude use of Etags on HTML, such as:
- cache-extending short-TTL resources
- making optimizations tuned to the specific browser
- optimizing in the background after first view, to avoid making the first client wait for optimizations to finish
We feel that all three of these values are more important than Etags. So while PageSpeed Insights might give us a negative score for the HTML etags, we'll get positive scores for long-cache-ttl resources & aggressively optimized images (webp). Also, this is not reflected in the PageSpeed score, but we achieve all of this without waiting for HTML to finish optimizing before sending results to the first client to view a page, which is critical for the usability of the product.
And in the end, I've never heard of a significant overall loss of PageSpeed Insights score due to turning on mod_pagespeed. You can of course construct that scenario due to stripping etags from an otherwise fully optimized page, but I don't think it makes sense to worry about that corner case.
-Josh