Let's see here.
Benefits: Your data is managed by experts whose main focus is keeping everyone's data secure, available and reliable. Multiple servers ensure redundancy and if needed globally available to allow for minimal latency.
"you have no control over", "is [a file] actually properly deleted"
Is this any different than trusting your local IT professional? What would be the fallout it if your AWS, Azure, Google, ect... was found to not treat a customers data in a secure and private way (please don't use a counter example from a middle tier service like iCloud, one drive, or google drive)?
"If the cloud is attacked, how long will it take for the parent company to admit they were hacked?"
A lot sooner, now that the EU is putting GDPR into place.
-- A personal opinion from your friendly Azure engineer