To make things worse, the opinionated nature of systemd's founder (Lennart Poettering) has meant many a sysadmin has had to fight with it in real-world usage (eg systemd-timesyncd's SNTP client not handling drift very well or systemd-networkd not handling real world DHCP fields). His responses "Don't use a computer with a clock that drifts" or "we're not supporting a non-standard field that the majority of DHCP servers use" just don't jive in the real world. The result was going to be ugly. It's not surprising that most distros ended up bundling chrony, etc.
It is not complicated at all. Recent enough versions of systemd support journal forwarding, but even without it, configuring rsyslog is extremely easy:
1. Install rsyslog
2. Create a file /etc/rsyslog.d/forwarding.conf
$ActionForwardDefaultTemplate RSYSLOG_ForwardFormat
*.* @@${your-syslog-server-here}:514
3. Restart rsyslog4. Profit.