"LiteMage purged tags cat_p_4784" like log lines should be generated by LiteMage. but your question seems to be "why Magento cron logging doesn't work?", is it(if so, Magento cron logging doesn't control by LiteMage)? or you want to see more logs from LiteMage? If not for both, can you clarify your question and your situation a little more?
Is there any way to have magento.cron.log contain anything else than LiteMage tag purges?
From my understanding, magento.cron.log is supposed to contain errors from the cron runs and errors only - in other words, no output from successful runs. The output from the LiteMage appears to be a regular output message and should therefore not end up in the error log.
My questions are:
1) Since it still ends up there, is the module logging what it interprets as an error, or is it just a regular output message.
2) If the module logging an error, how can we see what the error is when it's logging a regular output message instead of the error.
3) If it's not an error, is it "overwriting" errors from other modules by forcing regular output to the error log?
As described on the page you linked to earlier, the cron job is:
* * * * * /usr/bin/php /var/www/html/magento2/bin/magento cron:run 2>&1 | grep -v "Ran jobs by schedule" >> /var/www/html/magento2/var/log/magento.cron.log
As I'm sure you know, the -v means invert match, so any other output than "Ran jobs by schedule" will be logged. From what I understand, this is so that the log file will contain error messages from modules if something went wrong. What is the point of filling up the log with successful runs? If there were no errors, the run was successful - there's no need to output this.
But please reply to my questions above if you can.
If I understand you correctly, you want LiteMage to output less only when errors, right? Please log a ticket with us with tmp root ssh login and your magento admin login. We will check your settings. If it is something our LiteMage can be improved, we will forward to our developers.