What about user-mode Linux containers?
User Mode Linux (UML) - You could do that but at that point IMHO you might as well just run in qemu; UML is annoying to work with and performance isn't great.
Containers (of the sort popularized by docker and kubernetes) without root: As sibling comment says, this is that; from the kernel's view, manually calling unshare yourself looks the same as what podman or rootless docker do.