You haven't been paying attention these last 20 years when every unix vendor has replaced SysV init with something else.
Writing init scripts is not a one time annoyance, at least not for distro maintainers. They are also not portable between distributions, as systemd unit files are. SysV init is also literally the dumbest form of init, where the init process has no information about dependencies, and cannot react sensibly to any changes in system state. Another sticking point involved the inability of the system to track processes accurately, which resulted in a number of kernel-level features over the years, of which cgroups are merely the most recent. Yes, it's fairly rare to have things go wrong, but pidfiles are unquestionably a bad hack.
Init is a misnomer. It was supposed to be the method by which your system changed states, but it was never very good at this, so people are used to thinking of it only as handling a few rare circumstances. The problem systemd solves is how to get the computer from state A to state B reliably, and guarantee that the services it manages are started properly. Startup and shutdown are special cases of this problem. It is built on kernel-level features that allow it to track processes accurately (and incidentally also track resource useage).
Systemd is the result of a number of (IMO) obvious choices. Cgroups exist, therefore it makes sense to write a service management tool to take advantage of them. As long as you're writing a service management tool, you should probably write in dependency resolution. Handling startup and shutdown is another logical choice. Also, since 95% of init script contents are common tasks, it makes sense to abstract out that stuff into a common C-based library. At this point it is relevant to note that, cgroups aside, OpenRC does this exact same thing.
Writing scripts is part of UNIX, and systemd coexists with them pretty happily. However, rewriting scripts into more flexible C libraries is also part of the UNIX tradition. What's so hot about these scripts, besides that you're more comfortable working with them?