@dillfunlap
You describe a behavior that is more appropriate for a timer (an event that needs to happen at a specific time).
Schedule means a desirable situation from the activation of the schedule to the end.

Since there are events where a schedule behavior is not appropriate, as you say, i think the better solution is to add a checkbox to the schedule settings to indicate that is a "constant" schedule so even when the schedule is activated after the original start time the event handlers should be triggered.