So as of right now, there still doesn't seem to be some native way to teach GKE to enable NV. Between the time of your post and now, Nested Virtualization went GA sometime in April but they still mandate a image/license requirement to enable by design. I was hoping that they would enable it by default and that the managed Kubernetes images would pick it up as a side-effect but that did not happen.
That said, Hussain, your workaround is working great for my initial tests. I may not have 100% management, but I still have a lot of it and a Kubernetes+Containers API that CI systems are cognizant of. I don't think I've seen workaround steps like what you've described before during my search.
For my use case, I am also using it for nested virtualization testing, but also for testing IO inputs and outputs of a popular, larger, and common desktop OS with qemu. It's simply easier to manage auto-scaling clusters with Kubernetes and CI systems are generally aware of it.