Hi @CalvinS ,
Thanks for the idea. I fear that is not at all easy to implement. When an instance is stopped, the Hyperion API no longer reports any state about it. Home Assistant relies on this state (so it can know if the light is on/off/brightness/color/effect). In fact, when an instance is stopped, the current version of Home Assistant will actually remove the entity entirely because of this (and add it back when the instance is re-enabled).
What you describe is definitely not impossible, just quite difficult, so unless it was heavily sought after by others it may not get done. It might be good to open a bug against Hyperion itself (https://github.com/hyperion-project/hyperion.ng) as a simpler fix might be for Hyperion to not do whatever processing it is doing when the output is disabled (but keep the API available).