What is the idea here, exactly?

First off, we aren't asking for this to enable us to delete valid sprints!

Now that we have that out of the way ...

There can be cases where you accidentally switch to a new sprint when your previous sprint had 0 points. This screws up your sprint history and velocity average. So we'd like to be able to simply delete the sprint. The workaround of course is to compute your own velocity avg, ignoring the bad sprints, and enter it as the velocity estimate for the current sprint. Still, cleaner to have some ability for admins to delete sprints from the Sprint History page.

Deleting a sprint would have side effects. Stories in that sprint would automatically go back into the product backlog, because soties are identified as done, when they are assigned to a closed sprint.

We could enable deleting old sprints when there are no stories inside. Would this solve the problem?

Yeah that would solve it for us. The sprints we're talking about deleting are empty anyway.