Not everyone can manage a database properly and, sorry to say this to you but, Docker is a terrible idea for a database in general. Setting up your own database somewhere still puts your trivial data on someone else's server more or less.
All these "Serverless" keywords pretty much mean you don't have to be spinning up servers (cloud) or setting up & maintaining one. Nothing is "Serverless" per-se so it's time to move on from picking on this, I agree, bad choice of words.