Systems which do not use systemd simply do not have these problems because there is no analogous component. If syslogd goes down, the worst that happens is you don't get logs. Init doesn't go down because it essentially has no inputs. Individual services can go down if they're poorly written, but they won't bring the system down with them. Traditional systems (the hideousness that is "sysvinit") have plenty of other different problems (e.g. race conditions in process supervision), but deadlock or bringing down the whole system is not one of them.

With systemd on the other hand, all of the components under the systemd banner are tightly interconnected and communicating. In particular pid 1 has ongoing communication with multiple other components, and misbehavior from them can, both in theory and in practice, deadlock the whole system. In case you missed it, this is roughly what "monolithic architecture" means: even though the components are modular, they're designed for use in a tightly interwoven manner that's fragile. It's completely the opposite type of "monolithic" from the kernel, which has everything running in one address space, but with architectural modularity, where interdependency between components is kept fairly low.