I don't think it's the case yet. GDPR will enforce the right to be forgotten and as such truly delete data about you, but other than that, I don't think there are other regulations forcing you to delete data.
There are plenty of cases where a system would not function correctly if you are actually erasing DB entries when a user clicks the delete button. In many cases, even the users themselves might expect to be able to undo or go to a delete list and see entries that were deleted.