> Are there any examples of a process supervisor that isn't also intended to replace the traditional init system?
Yes. You are conflating System 5 init and System 5 rc.
The IBM AIX srcmstr program is intended to be run by init, not to replace it. ("The SRC is operationally independent of the init command." - http://www-01.ibm.com/support/knowledgecenter/ssw_aix_61/com... "You can also start the SRC from the command line, a profile, or a shell script, but there are several reasons for starting it during initialization" - http://www-01.ibm.com/support/knowledgecenter/ssw_aix_71/com...)
Gerrit Pape's runit has "runit" (exec()ed from "runit-init") as a system manager running as process #1 doing the system management tasks that only process #1 can do, and "runsvdir" as a service manager that runs as some other process.
Daniel J. Bernstein's daemontools, Adam Sampson's freedt, and Bruce Guenter's daemontools-encore do not, strictly speaking (and pace Paul Jarc's patches), have a program for running as process #1. They all have "svscanboot", which is to be spawned by process #1 and which runs "svscan" as a service manager.
Laurent Bercot's s6 does not have a program for running as process #1. Its "s6-svscan" is a service manager, usually run as some other process. And its "s6-svscanboot" sample program is analogous to "svscanboot". It comes with examples for writing one's own program to run as process #1, but "s6 cannot provide live examples without becoming system-specific" (http://skarnet.org./software/s6/s6-svscan-1.html).
Wayne Marshall's perp has "perpd" as the service manager. This can be started by "perpboot", which (like "svscanboot") is spawned by process #1 rather than run as process #1. There's no program in the package for doing process #1 tasks.
nosh has a program for process #1, "system-manager", and a program that runs in another process to do service management, "service-manager".
All of these aim at replacing System 5 rc. Only two in fact offer in-the-box replacements for System 5 init. Do not conflate rc and init. The person that you were replying to was wrong; hence the basis for your question was wrong. Learn from "system-manager"'s manual page, "runit"'s manual page, what Paul Jarc found when he experimented with running svscan as process #1, and indeed "systemd"'s manual page to an extent. "init's job" is more than "starting a process supervisor".