This article does a great job describing the investment required to pull this off. At HubSpot, my team is running a large Vitess/MySql deployment (500+ distinct databases some sharded, multi region) atop k8s today and had to learn a lot of those same lessons and primitives. We opted to write our own operator(s) to do it. In the end, the investment has paid off in terms of being able to build self service functionality for the rest of the business and write the kinds of tools workflows that allow us to support it with a relatively small team. The value is in the operator pattern itself and being able to manipulate things on a common control plane. Compared to the alternative of managing this with Terraform and Puppet/Ansible/Chef directly on EC2, which I've also done before, it's a better experience and much more maintainable even at the fixed expense of additional training and tooling.
I won't disagree with others that RDS is probably worth it until you need something very specific or have reached a certain scale.
Happy to share tips or pointers for anyone going down this path specifically with MySql or database workloads in general.