I think you're conflating "infinite growth" with "unsustainable."

Advertising can be a sustainable business model. Radio, television, billboards, etc. sustain themselves through advertising. We can quibble about their growth rates, but if advertising were unsustainable, then these industries wouldn't exist in their current form.

I think you're actually rejecting the idea that a company can sustain infinite growth through advertising. I think that's a little different from being wholly "unsustainable."