Agreed, this is a standard option on most autonomous network servers. Not really hard to implement either on sender or receiver end. Few lines of python code.
I’m not sure about solution described below, however I have found that recent (last year or so) updates to Home Assistant log file handling code made it difficult if not impossible to capture the last log entries at crash or HA shutdown/restart. These are often critical to debugging issues. I think any wrapper around a text file monitoring solution/hack has the potential to not capture all log records. The core system has to make sure it writes these last will and testament messages before dying or exiting. The roll over of one prior log file helped a little, however the login history of unix/linux logging shows that more control over logging options should be standard here.
IMHO, log messages in Home Assistant could use some love in general. They often do not point to the source of the message, just the error. And dumping raw python multiline exceptions into the log file make overall monitoring of server painful.