Well said. I'd add that "service" is actually doubly confusing because the command was IIRC actually introduced by Ubuntu when they were doing Upstart, which was their own attempt an an init replacement. Ubuntu still has the service command, actually, and now it supposedly runs both init scripts and systemd units. I've never actually tried it because I'm rather spooked by having multiple mechanisms to activate a service. It still mostly has the upstart command syntax from what I can recall.
My Ubuntu server actually has a Upstart service file from one of the daemons I have installed, I only hope it's not somehow being activated or translated into an init script by some compatibility system Ubuntu has built in.
You might even be talking about RHEL 6, in which they used Upstart, and not whatever they're doing now. RHEL 6 is still under extended support, which means that there are still quite a lot of Upstart systems out there.
OTOH, I wouldn't be surprised if every other feasible approach's downsides are widely regarded to be worse.
Software. Yay :D
I have no complaints about distros that are either 100% systemd or 100% init scripts. The problem with Debian (and its derivatives) is that they're trying to maintain both at the same time.
If they really want to support both "/etc/init.d/servicename start" and "systemctl start servicename" commands, one should be turned into an empty shell that simply invokes the other, like what Red Hat did with the "service" command. The current system kinda works out of the box, but goes out of sync as soon as you try to customize either the init script or the unit file.