TYPO3 Core

That of course would be very nice, but I don't see how this could be done with the current structure of the EM.

maybe using the update wizard?

That's a possibility, yes. What I don't like with the EM's update mechanism is that it cannot be launched automatically. Maybe it could be achieved by (mis-)using user-defined configuration options.

abusing any of these systems is not an option. I'll work on something to achieve this for 4.4 I guess.

If the task can only be added as disabled then there's no point in having it really. After all you want to do certain things periodically for a reason. Yes, of course someone could do stupid things with it, but there are enough ways to do that otherwise as well. Let's try to trust people first.

An alternative would be to have a popup during installation similar to those dialogs you find with OAuth... Application FooBar would like to do A, B, and C. Which of these things do you want to allow? (All checked by default). This would be super user friendly. Something would need to get figured out for non-backend EM installations.

Maybe it would also be possible to add another section to the Scheduler Module called "Suggestions" where extensions could suggest crons with interval, arguments etc. so you would just have to click a "+" Icon in the end to add this specific task with the suggested settings. Also there should be a second button like "Add and Modify" which opens an edit view for the task prefilled but let's the user change settings before adding the task.

Just giving extensions the possibility to add active scheduler tasks would open up doors for nasty conflicts between extensions I think. Also certain extensions could be used for multiple purposes and an extension author might only have one of multiple purposes in mind.