A combination of things, mostly related to Kubernetes' scope and use case being different from Ansible/CFEngine/etc. Kubernetes actually runs your environment. Ansible/CFEngine/etc. set up an environment that runs somewhere else.
This is basically the benefit of "containerization" - it's not the containers themselves, it's the constraints they place on the problem space.
Kubernetes gives you limited tools for doing things to container images beyond running a single command - you can run initContainers and health checks, but the model is generally that you start a container from an image, run a command, and exit the container when the command exits. If you want the service to respawn, the whole container respawns. If you want to upgrade it, you delete the container and make a new one, you don't upgrade it in place.
If you want to, say, run a three-node database cluster, an Ansible playbook is likely to go to each machine, configure some apt sources, install a package, copy some auth keys around, create some firewall rules, start up the first database in initialization mode if it's a new deployment, connect the rest of the databases, etc. You can't take this approach in Kubernetes. Your software comes in via a Docker image, which is generated from an imperative Dockerfile (or whatever tool you like), but that happens ahead of time, outside of your running infrastructure. You can't (or shouldn't, at least) download and install software when the container starts up.
You also can't control the order when the containers start up - each DB process must be capable of syncing up with whichever DB instances happen to be running when it starts up. You can have a "controller" (https://kubernetes.io/docs/concepts/architecture/controller/) if you want loops, but a controller isn't really set up to be fully imperative, either. It gets to say, I want to go from here to point B, but it doesn't get much control of the steps to get there. And it has to be able to account for things like one database server disappearing at a random time. It can tell Kubernetes how point B looks different from point A, but that's it.
And since Kubernetes only runs containers, and containers abstract over machines (physical or virtual), it gets to insist that every time it runs some command, it runs in a fresh container. You don't have to have any logic for, how do I handle running the database if a previous version of the database was installed. It's not - you build a new fresh Docker image, and you run the database command in a container from that image. If the command exits, the container goes away, and Kubernetes starts a new container with another attempt to run that command. It can do that because it's not managing systems you provide it, it's managing containers that it creates. If you need to incrementally migrate your data from DB version 1 to 1.1, you can start up some fresh containers running version 1.1, wait for the data to sync, and then shut down version 1 - no in-place upgrades like you'd be tempted to do on full machines.
And yeah, for databases, you need to keep track of persistent storage, but that's explicitly specified in your config. You don't have any problems with configuration drift (a serious problem with large-scale Ansible/CFEngine/etc.) because there's nothing that's unexpectedly stateful. Everything is fully determined by what's specified in the latest version of your manifest because there's no other input to the system beyond that.
Again, the tradeoff is this makes quite a few constraints on your system design. They're all constraints that are long-term better if you're running at a large enough scale, but it's not clear the benefits are worth it for very small projects. I prefer running three-node database clusters on stateful machines, for instance - but the stateless web applications on top can certainly live in Kubernetes, there's no sense caring about "oh we used to run a2enmod but our current playbook doesn't run a2dismod so half our machines have this module by mistake" or whatever.
This is basically the benefit of "containerization" - it's not the containers themselves, it's the constraints they place on the problem space.
Kubernetes gives you limited tools for doing things to container images beyond running a single command - you can run initContainers and health checks, but the model is generally that you start a container from an image, run a command, and exit the container when the command exits. If you want the service to respawn, the whole container respawns. If you want to upgrade it, you delete the container and make a new one, you don't upgrade it in place.
If you want to, say, run a three-node database cluster, an Ansible playbook is likely to go to each machine, configure some apt sources, install a package, copy some auth keys around, create some firewall rules, start up the first database in initialization mode if it's a new deployment, connect the rest of the databases, etc. You can't take this approach in Kubernetes. Your software comes in via a Docker image, which is generated from an imperative Dockerfile (or whatever tool you like), but that happens ahead of time, outside of your running infrastructure. You can't (or shouldn't, at least) download and install software when the container starts up.
You also can't control the order when the containers start up - each DB process must be capable of syncing up with whichever DB instances happen to be running when it starts up. You can have a "controller" (https://kubernetes.io/docs/concepts/architecture/controller/) if you want loops, but a controller isn't really set up to be fully imperative, either. It gets to say, I want to go from here to point B, but it doesn't get much control of the steps to get there. And it has to be able to account for things like one database server disappearing at a random time. It can tell Kubernetes how point B looks different from point A, but that's it.
And since Kubernetes only runs containers, and containers abstract over machines (physical or virtual), it gets to insist that every time it runs some command, it runs in a fresh container. You don't have to have any logic for, how do I handle running the database if a previous version of the database was installed. It's not - you build a new fresh Docker image, and you run the database command in a container from that image. If the command exits, the container goes away, and Kubernetes starts a new container with another attempt to run that command. It can do that because it's not managing systems you provide it, it's managing containers that it creates. If you need to incrementally migrate your data from DB version 1 to 1.1, you can start up some fresh containers running version 1.1, wait for the data to sync, and then shut down version 1 - no in-place upgrades like you'd be tempted to do on full machines.
And yeah, for databases, you need to keep track of persistent storage, but that's explicitly specified in your config. You don't have any problems with configuration drift (a serious problem with large-scale Ansible/CFEngine/etc.) because there's nothing that's unexpectedly stateful. Everything is fully determined by what's specified in the latest version of your manifest because there's no other input to the system beyond that.
Again, the tradeoff is this makes quite a few constraints on your system design. They're all constraints that are long-term better if you're running at a large enough scale, but it's not clear the benefits are worth it for very small projects. I prefer running three-node database clusters on stateful machines, for instance - but the stateless web applications on top can certainly live in Kubernetes, there's no sense caring about "oh we used to run a2enmod but our current playbook doesn't run a2dismod so half our machines have this module by mistake" or whatever.