As someone who's administered Solaris machines rather extensively, I find the SMF (the init system on Solaris which, in part, inspired systemd) to be much easier to manage than sysvinit. Specifically, it makes it easier to add new services than either writing new shell scripts or adapting old ones. It makes it easier to make services which depend on one-another. And it makes it easier to know which services are running and what state they are in.
I see other developers/sysadmins here saying that sysadmins usually have a template initscript which they can use to author new ones, but that's really still a lot of work if you want to do anything not covered by the template and it leads to duplicate code. (It's literal cut-n-paste programming.) Initscripts expose a lot of implementation details. Even worse, they're different for every Linux distro so the initscript for your application has to be different for every distro you want to be on.
I think the most telling thing here is, that the distro maintainers, who are the ones who write the bulk of the initscripts for Linux systems, are the ones pushing for the adoption. It's making their lives easier.