TL;DR - today the CNI itself is interface to network implementation, so you'd need a minimal one.
But you do not need a "complex" CNI. Originally k8s pretty much worked with assumption you can route few subnets in good old static way to the cluster and that's it, and it works with that kind of approach still - each node gets a /24, there's a separate shared /24 (or more) for services, etc.
The complexities came from the fact that a lot of places that wanted to deploy kubernetes couldn't provide such a simple network infrastructure to hosts, then later what was a workaround got equipped with various extra bells&whistles
But you do not need a "complex" CNI. Originally k8s pretty much worked with assumption you can route few subnets in good old static way to the cluster and that's it, and it works with that kind of approach still - each node gets a /24, there's a separate shared /24 (or more) for services, etc.
The complexities came from the fact that a lot of places that wanted to deploy kubernetes couldn't provide such a simple network infrastructure to hosts, then later what was a workaround got equipped with various extra bells&whistles