Maybe this feature exists and I just don't see it, but it would really be handy if on my HTC the "normal" status updates would remove the "elevated" and "critical" updates as to clear the phone vs. having to manually delete each one.  

In settings, there is a 'Clear badges on exit' toggle. However, they will re-appear again if the issue is not resolved. Hope this makes sense

Hmm.  I logged into the Monitor and the Dashboard but I am unable to find the "Clear badges on exit."  

On the iPhone, there are 4 options at bottom (Systems, Notifications, Reports, Settings). Tap Settings and within there you will find it.

On the Android we have 4 as well listed as Set Filters, View Groups, Settings, & Share This App.  I do not see an option anywhere that allows a restored status alert to remove the corresponding elevated/critical alert.  

On android you don't have app badges that indicated notification count. To clear the notification count make sure you acknowledge each notification (just open it) and the notification count will decrease.