On the other hand RDS hides a lot of the complexity from you. You don't have to pick an OS, apply updates, secure it, manage it, configure it, or patch it. There are some number of virtual servers out there that are nominally running your RDS cluster, but it's all pretty theoretical.
So I'm not entirely understanding your point.
> you need to pay to have an instance running per hour
You are paying to have instances running with every other DB service too; they may just break it out on your bill a bit differently. :)
The real issue with RDS for me isn't that they haven't removed the server part from the equation (they have), it's that they haven't removed the RDBMS from the equation. Schema changes, data migrations, replicas, sharding, scaling: All the hard parts of running a RDBMS are still there.
If Amazon could somehow make a magical service that accepted SQL queries and somehow returned my data, I'd be ecstatic - but the difference between that and RDS isn't the fact that they're letting me know how much ram the virtual server which is nominally running MySQL for me has.
What I'm getting at is, a hosted DB is a hosted DB.. What makes SQL unsuitable for serverless?
Anyway, my bad, I now see your point :)
Touting "serverless" as some sort of mysticism that doesn't really mean anything useful doesn't really get anybody anywhere.