I just wonder what chances any new general-purpose OS kernel may have against Linux.

I suspect that whatever replaces Linux will probably involve a paradigm shift at the lowest level. Perhaps capability-based IPC, perhaps seamlessly integrating local and networked nodes, etc. It’s going to take major major improvements to move the world off of the Linux kernel.

I imagine it's going to be an exokernel that can run pretty arbitrary user lands as if they were containers, built on cap based security.

If anyone agrees with me and wants to help out making that happen on an open source code base, hit me up.

Have you looked at https://github.com/nanovms/nanos yet? What you are describing is fairly close and this is under active development.