A shell script _is_ a way of specifying what binary to run. It's just that it's standardised and relatively well thought-out, as opposed to one-off hacks, like with systemd.
Pretty much the only thing about shell scripting that is useful and not easy to do in other languages is input/output redirection and piping. Service managers should take care of things like figuring out where stdout and stderr logs are sent to, so you shouldn't have to do that stuff in your service scripts.
Thus there is no benefit to shell compared to other languages / formats, and there are a lot of problems with shell scripting otherwise.
You don't have to. The fact that Linux had anachronisms like that wasn't because of shell scripts, it's an entirely orthogonal issue; a typical rc script in, say, FreeBSD, looks like this: https://github.com/freebsd/freebsd-src/blob/main/libexec/rc/.... It's declarative, it's easy to understand, but it also provides you with flexibility when you need it, as opposed to one-off hacks with custom, fixed functionality and random syntax.