EventBridge Notes
Flexible Timeframes
The flexible timeframes feature on EventBridge is there to help avoid having e.g. a bunch of tasks all executing at the same time (which could, for instance, cause heavy load on a user's database servers).
It's not there to balance out load on AWS resources, just on the user's resources downstream.
IAM roles for EventBridge Schedules
If you delete an IAM role (e.g. to rename it), you won't get any obvious notifications, but the EventBridge Schedules that use said role will stop working, as they'll be unable to execute.
You need to go through each of the affected schedules and re-assign the new IAM role in their Settings pages.