Why would you argue? Selecting only the successes is the literal definition of cherry-picking. I'd say that every one of those cherries is very arguable, though, especially if one's definition of successful has any relation to being profitable.
True, although I feel like none of those products have made positive product-oriented changes in many years now. Gmail at least is spiraling down the product toilet, which makes me really sad.
Google doesn't have an ad-business, it is an ad-business.
You can't separate Google from its ad business. All of their major products exist in service of the ad business, search, inbox, even Chrome. If the services don't exist to help build a profile of you, they exist to help build a profile of web traffic and detect ad-fraud, or to simply shape the landscape into one that isn't hostile to google's ads.
I'd say that Google has these products (really, services) because of its ad business, not the other way round.
Someone more familiar with Google's oeuvre can probably answer this: all those well-liked services that Google unceremoniously cancelled — were they the ones that didn't help (or harmed) Google's ad business?