4 answers
I can understand why Management would not want Users to delete opportunties, because they might start deleting Lost Opportunties to make their numbers look better or something like that. But this would mean that yu would lose the historical record that a Prospect or Client was pursued and that it did not go anywhere (and that information is still important)
For thise reasons on our SFDC org we do not allow users to delete Opportunites. However having Opportunties that were created by accident, or that were duplicates, etc is almost as bad. So on our SFDC org users can submit a "Delete request" to Sales Operations and Sys Admin is allowed to delete them (but only for specific reasons).
I would talk this over with the people in Management who are saying that No Opportunities should ever be deleted. Because having crappy, bad data in your SFDC or is never a good thing, and that's what this will cause.