Hi,
I've found two issues with administration modules and I'm interested if anyone else is having them:
Administrator modules caching
When enabled caching in global configuration, there are no cache entries created for administration modules.
Many modules don't allow any caching method (Caching: No caching), but some (like mod_quickicons) inherit caching method from global configuration.
I've tested in Joomla 3.4.8 and Joomla 3.6, logged as user in Super Users group and reloaded admin panel main page. Only folders created in cache folder are:
_system
com_plugins
fof
Statistics module
Another issue is that the module mod_stats_admin (Site information) doesn't show up in control panel.
I fixed that by changing it's original access from Super Users to Public and then back to Super Users. I don't remember ever seeing this module in fact I didn't knew it exists.