If it's just a single server, you're fine with logrotate and grep.
Who said graylog is only logging on that single server? That server is by far the biggest and hence why I run multiple services with big dependencies on it, but I have that server, 2 cloud servers (one running my personal web page and other publically accessible services, one running a couple of game servers) + a couple of Raspberry Pis.
Even if I didn't have all that, a web interface to configure it to email on ssh login or send me a mobile notification that my offsite backups are still happening and/or not happening for devices or similar items would still be a nice feature, even if you personally feel it's too complex or you could write a cron job for each of them.