I think it is better for MS Flow to send the owner an email if the MS flow fails to execute.
A MS flow fails to execute may be due to the connector permission has expired.
But current there is no way for the owner of the ms flow to know this unless he/she goes to the flow site checks everyday.
This is a must have especially because you cannot build this by yourself. You can't build an "error path" via mail alerting because you don't know whether the connector permission for Outlook has already expired and then the flow wont send anything (despite the "Your flow failed x times" mail message)
This idea can be merged with https://powerusers.microsoft.com/t5/Power-Automate-Ideas/Access-to-Flow-Status-as-a-connector/idi-p/...