But that's exactly what happens with docker anyway (e.g.: Docker is still running in the Linux VM when running it from a different operating system). And considering the widespread systemd adoption throughout the Linux ecosystem, it's far more likely for systemd to be already installed in the VM than docker anyway.
Systemd docker-replacement on a non-systemd Linux would need to run in a VM, though.
Systemd-docker-replacement: works only on systemd-Linux. Tooling for any other arrangement, including non-systemd linux, left as an exercise to the user.
Docker: works on Linux—systemd or otherwise. Has tooling to making working on macOS or Windows non-terrible and lets you use (mostly) the same commands as you would on Linux.
I'm saying that cross-platform tooling is what makes Docker Docker. Systemd can't replace it without replacing the tooling, even if it can do the same thing only on systemd-Linux.
Would it? There's no reason this hypothetical systemd-docker-replacement couldn't be architected in a way that would not have a runtime dependency on systemd-the-init-system.
In any case, I'm not even sure if systemd wants to be a docker replacement (although it does seem to pick up more and more container features lately). But there's definitely some overlap between the two projects (in particular around process/service management) but podman is a much more direct competitor to docker than systemd.