Most services just need the init system to start, stop and monitor them. There's no special integration needed for each of them beyond running a command, monitoring the PID, and killing the PID when it's time to stop.

If you mean the special integration of docker and podman with systemd, first of all that's only required in rootless mode and not everybody runs rootless (most users probably run root docker). In rootless mode you have to manage each container individually as if it were a standalone service instead of just managing docker. Basically you have to integrate each container into the init system, whatever that is. There are some tools that make it easier to with podman+systemd because they write the systemd units for you but you can do it with any init system. The distro mostly doesn't care because you have to do the work not them.