Feature request/proposal: Downtime until OK/UP

I'd like to propose a new feature for downtimes (or a new type of downtime):
The possibility to define a downtime that stays as long the host/service is in a problem state and automatically gets removed when it switches to UP/OK.

Our use case for this would be the following:
Currently we have hundreds of virtual desktop servers (terminal servers) that automatically scale (get shut down/booted up) based on the number of sessions needed.
As they always stay in the monitoring, we need to set downtimes when they shut down. This is done via a shutdown script on the host against the Icinga 2 API.
On boot the inverse happens. The downtimes need to be removed. This is another script, getting the downtimes (only those created by the shutdown script), triggering all checks (to get them into an OK state to prevent false-positive notifications on old states) and then remove the downtime objects.

With this feature the startup script and its API calls would become obsolete. And I could imagine that there are other use cases as well :)

The issue names no source files or tests; start by tracing how downtimes are created, evaluated, and removed through the Icinga 2 API. Compare the proposed lifecycle with existing downtime behavior and the shutdown/startup scripts described here. Done means a downtime can persist while a host or service is in a problem state and is removed automatically when it reaches UP or OK.