The ads division is mostly firewalled off from the daily concerns of people developing products at Google. They supply cash to the treasury, people think up cool ideas and try to implement them. It works just like startups, where you don't always know what your business model is going to be. Gmail started as a 20% project, not as a grand plan to create an ad channel. Lots of projects and products at Google have no business model, no revenue model, the company does throw money at projects and "figure it out later" how it'll make money.
Do you think Johnny Ive, when designing the Apple Watch is concerned more with the business side of how they'll up-sell different watch bands to make money, or do you think he is absolutely focused on delivering a product experience that is fantastic and that if they do a good job, the business will do well?
Someone may figure out how to shove ads into Inbox later. There are separate teams who figure stuff like that out. But those people are not the ones who control the product features, purpose, or design goals. They don't come to us and say 'Hey, we want to sell more ad space in Gmail, do you think you could come up with a UI to cluster emails so we can surface more ads?' That is not how things work. Products start with ideas to solve user problems, not with ads.
Notice, G+ has been out for years and still doesn't show ads. Do you think G+ was designed to show ads? It was not, otherwise it would have shown them already. Someone will retroactively figure out how to do it at some point. In the same vein that Twitter was launched without knowing how they'd put ads in it.
Products at Google, from Search, to Mail, Calendar, Docs, et al are designed primary to help users. If we do a good job, we will retain our user base, and someone will figure out how to convert that to revenue, be it ads, or direct payments.
Ads are a necessary evil, but they are not the primary motivating force driving designs or features, either inside Google, or in the wider startup community.