Having done exactly that in the past, both by hand and with configuration management (including custom scripting that synchronized HAproxy configs etc.), I would say that I can do all of that much, much simpler in k8s.
Installing application and routing it with load balancing, TLS etc and support for draining is really simplified, something that used to require annoying amount of time (it got better as Lua scripting was extended in HAproxy, but by that time I also had k8s).
Resource allocation, including persistent storage (including NFS) is so much easier it's not funny, it makes my old years painful to think about. Syslog is not novel but getting all applications to log the same way was always a PITA, and at least with containers it's a bit easier (I still have to sometimes ship physical logs from containers...).
As for monitoring, that's one of the newer and more advanced topics, but it's possible to integrate more complex server monitoring with k8s - it already provides a lot of OS/application side monitoring that really makes it easier to setup observability - but now there's quite simple way to integrate custom node states into kubernetes allowing a quick glance way to check why a node is not accepting jobs, integrated with the system so you can actually trigger from a health-check that the node is in trouble and should not take jobs.