I also used to hate the phrase. But now I get it. And it's not about marketing, but about the idea that the developers _doesn't shouldn't have to worry about the server_.
For example, when you run a DB on a classic DBaaS, you have to worry about CPU, memory, storage provisioning. But when you use a classic SaaS service (e.g., Stripe, Twilio), you don't think about servers at all - but rather just how much you are consuming.
The Serverless model for databases is aiming to apply a SaaS like experience but for DBaaS. Where you don't need to think about provisioning, but about consumption.
What we (try to) do in this article is to push beyond that serverless paradigm. We believe there are real drawbacks to the "serverless black box" architecture that the industry is building, and what (we believe) developers need (including ourselves) is a more a "transparent box."
Hope this helps. But "serverless" also feels a little like "horseless carriages". I suspect in 5 years we'll have a better term that describes this concept for what it _is_, not what it _isn't_.