I've been working on this for the last year or so: https://github.com/desultory/ugrd

It's mostly made to work with Gentoo (uses pax-utils for finding dependencies), but should work with any distro. It does most of the initramfs creation process rootless. The main consideration is that you need privileges to make device nodes, but I just create them synthetically within the cpio image.

On most systems, this tool still requires root to copy the mount binary.