minimal init daemon by rich felker, author of musl libc

init.c

#define _XOPEN_SOURCE 700
#include <signal.h>
#include <unistd.h>

int main()
{
	sigset_t set;
	int status;

	if (getpid() != 1) return 1;

	sigfillset(&set);
	sigprocmask(SIG_BLOCK, &set, 0);

	if (fork()) for (;;) wait(&status);

	sigprocmask(SIG_UNBLOCK, &set, 0);

	setsid();
	setpgid(0, 0);
	return execve("/etc/rc", (char *[]){ "rc", 0 }, (char *[]){ 0 });
}

Is it not possible to straight up execute the /etc/rc script? Just by adding init=/etc/rc to the kernel command line?

You need a always running daemon, who will be reap a zombie. It is single work for init.
If you redirect this job to /etc/rc, you got a systemd again.
You cannot start an another daemon from /etc/rc for this. Zombie go to process with PID 1. /etc/rc have a PID 1 in your case.