For what it's worth, I have also managed my own databases, but that's exactly why I don't think it's a good use of my time. Because it does take time! And managed database options are abundant, inexpensive, and perform well. So I just don't really see the appeal of putting time into this.
If you have a database, you still have work to do - optimizing, understanding indexes, etc. Managed services don't solve these problems for you magically and once you do them, just running the db itself isn't such a big deal and it's probably easier to tune for what you want to do.