However with Kubernetes your infrastructure will be ready to scale. You need to expose both front-end and back-end services under the same host? No need to tinker with nginx configs, you just create two ingresses and do it in a standardized way. You need to run your service with two replicas and rolling zero-downtime update? Kubernetes has it out of the box. Good luck implementing all the necessary dances with custom docker-compose setup without dropped requests. You want to customize healthcheck? Kubernetes got you covered with all the imaginable scenarios.
The only missing block in Kubernetes is support for building containers. This is implemented with docker-compose extremely elegantly and simple. That I admit.