I don’t see any fundamental reason why systemd would be insecure.
You mean aside how the author answer to CVEs, right ?
If anything, I would expect it to be less prone to security bugs than the conglomerations of shell scripts that used to be used for init systems.
Not sure. In the end the shell script were just an easy and consistent way to start/stop programs. If the programs were secure (read: checked the input and sanitize it, did the check for permissions and so on) there is not a big difference.
Also, systemd performs way better than the old init systems anyway.
In what regards ? Boot faster ? Fine, but on a server it does not mean anything, a server does not reboot that often; for a desktop it not that the 5 seconds you gain are a fundamental gain.
One problem I see is with the logs: it is true that the format is documented, but a text format is always readable while a binary format... (been here, done that 🤬 )