I'm not sure Gmail is the right example here. When it came out, Gmail was way better than the other free email services (Hotmail, Yahoo, etc). It was the product that bent over backwards to deliver a great customer experience.
As a user, you were faceless. I have a vague memory from the early Gmail days. I'm pretty sure they charged me $5 to contact support.
Customer focus includes more than having a good product, though having a good product is a component. The business model Google chose (it was a choice) for Gmail wasn't compatible with focusing on Google's customers.
That said, there were other good examples. I chose Gmail because I believe it was one of the best known products of the era.
I'm embarrassed to say, I just realized the big problem with my original comment, and it is hackneyed: the end-users probably weren't the customers.
I doubt Google was cavalier about its relationships with advertisers back then.
Gmail in its early stage had a simple surface area. These days a Google account could mean a gateway to entire digital life for some. It requires much more focus and responsibility to handle and Google never had plans to do any of that from the beginning.