It's absolutely not true that the only reason to run a service like this is to tie usage to specific users. And you don't even need to assume that this is altruistic. Here are some concrete benefits to Google.
First of all, encrypted traffic allows circumventing content mangling middleboxes at operators. Sometimes those middleboxes are merely annoying (say Byte Mobile), sometimes outright evil (ad insertion / replacement).
Second, a faster web experience will mean more web usage in general, and that'll translate to more ad revenue for Google.
Third, faster (or cheaper) web usage is a competitive advantage. On one hand it makes Android more competitive against iOS and WP8 (and the bit players as well). On the other hand it makes Google Android more compelling than other Android versions. Not a big deal with Amazon's fork. Potentially huge if e.g. Samsung were considering a full fork.
That's a few off the top of my head. If you try, I'm sure you too can come up with more plausible explanations than "you're the product".
"note that secure connections (HTTPS) are routed directly from your mobile device to the destination, bypassing the optimization proxy – only HTTP requests are routed through and optimized by the proxy. Further, the use of the service does not require a Google account; navigation in incognito tabs bypasses the proxy; original IP address of your device is forwarded to the destination via the X-Forwarded-For header – the data compression service is a transparent proxy."
Without looking I can safely say it's not a public proxy, probably tied to your device's Google Accounts session.