If the user is allowed according with their contract or law to delete their account they should be able to request that themselves from within the app. This is what I understand from what Apple is requiring the apps to do. It is very similar with GDPR "Right to erasure"/"right to be forgotten".
For your specific cases:
- if a user rented something then they should not be allowed legally to close their account until they return or pay the equipment. If that is in the contract then the delete my account button should be disabled until their contract is terminated/closed.
- if you're a dog kennel it is the same, the user should keep the account until the dog is returned.
- if you are a parole division of the police and the "customer" by law can have their records deleted they should be able to do so.