Absolutely, but it's worth mentioning that it's not zero-cost for those providers. (I have no idea what their actual cost is, and I assume they take steps to minimize it...)
EKS is priced competitively, with Amazon's other offerings. I was a part of the chorus of voices saying "wtf Amazon, control planes ought not cost, nobody else is charging for them" but I think this is fairly priced for what it is... it only takes four reserved M4.large instances to eclipse the cost of an EKS cluster, and you will likely want more than that if you are aiming for real High Availability and trying to build it on your own EC2 nodes.
The default configuration of EKS is fully HA, AIUI is built to be resilient to faults like failure of an entire region.
If you don't want to pay for the Kubernetes API, the interop chances for engaging outside support that it gives you, and the associated complexity required to support it and keep pace with the release cadence, then there is also Fargate which is cheaper at low scale, (or my preference, go with the competition who have all agreed to undercut AWS, so why not take advantage as it's clearly favorable to run at least some of those workloads elsewhere.)
And hey, there's even Virtual Kubelet on Fargate if you want to get the best of both worlds, right? Of course that one comes with a big warning, DO NOT run any Production...
