I'm wondering though what value will Kubernetes add beside integrating with existing (presumably Kubernetes-based) infrastructure? At least, this is my understanding of the rationale for Kata containers. Other than that, it seems like it'd be just getting in the way...
Funnily that's what fly does: take your container uncompress it to a full micro VM and run it on their infra
Firecracker also has containerd support (https://github.com/firecracker-microvm/firecracker-container...).
There are a few ways to run Kubernetes with Firecracker, including FireKube.
(Cold) boot times are determined by a chain of components, including (1) the controller (eg, k8s/Borg), (2) the VMM (Firecracker, QEMU, Cloud Hypervisor), (3) the VM's OS (e.g., Linux, Windows, etc), (4) any initialization of processes, libs, etc and finally (5) the app itself.
With Unikraft we build extremely specialized VMs (unikernels) in order to minimize the overhead of (3) and (4). On KraftCloud, which leverages Unikraft/unikernels, we additionally use a custom controller to optimize (1) and Firecracker to optimize (2). What's left is (5), the app, which hopefully the developers can optimize if needed.