Escalation rules can solve many of the problems you mention in your request - by configuring multiple support departments and escalation rules, you can determine the behavior of a ticket after it reaches a certain age (ie 4 hours, 6 hours, etc). Some of this behavior includes notifying admins, sending the ticket to another department, and auto updating to a different status. You can find the documentation here:

We'll keep an eye on this request to see how it evolves in time.