Thanks for the feedback @James Ainsworth
From our point of view any feedback from customer (from email) is important to be aware of. Even if it is just a "Thanks, it's resolved".
Manual action is acceptable for these scenarios. (Unlike the fact that case owner today is not aware of the customers update by email.)
If an incoming email to a request within resolved status, automatically changes the status to for instance "Customer update", the operator can check the feedback and either close it or re-open it.
When adding the ability for an "updated from customer" status, operators could activly check this queue and address requests properly.
Notifications, and escpecially email to case owner is not preferably cause it causes a lot of noise.