"We just want to make the Web faster" is what they tell their employees so that otherwise ethical people will write code that does unethical things. (AMP/portals is another example.)
Or also, faster ads. The explanation that faster web better compete with native apps and make for better revenue.
(I agree that it is likely not the only factor, but it a reasonable one)
Just like Facebook, with its free basics internet deals with mobile providers in emerging markets, sought to confuse people into thinking Facebook is the internet, Google also sought to confuse people to think Google is the internet.
You've said it yourself: "the big selling point was being faster."
And yes, there is obviously some marginal value for Google in simply making web experience as fast as possible because it keeps people using the web. But that extended web use is of no good to them if users are doing so at non-Google properties that don't see Google ads, so it seems implausible that control was not a key motivator.
Extended web use is often punctuated by google searches, even if a lot of the engagement happens on non-Google properties. If slowness causes people to get bored and go do something else, Google suffers.
Disclaimer: ex-googler.