When check the alerts, some of them doesn't generate log files. Also, some log messages with severe level of severity should generate alerts but they don't do it.
It would be useful for Administrators to create alerts based on log messages and log levels. At the same time, ArcGIS Monitor must include an option to add exemptions to alerts because it is a known issue or something will be solved after patching or enhancement on services.
Just now, we have to analyze the log messages separately of ArcGIS Monitor and using scripting to be aware of errors and unexpected behaviors in ArcGIS Server or Portal for ArcGIS.