I would think not changing the organization of the ticket would be a good thing in most cases.
Add an option, but also a confirmation.
Are you sure you want to change this tickets Org to " "?
"Most cases." Problem is, if there are any cases, it needs to be able to be changed. You don't want ticket data going to the wrong entity. I can't think of any case where it would be okay to be locked.
That was my point, allow the change, but confirm it before it's set. You don't want a ticket getting moved from one org to another org with sensitive information in it, by mistake.
Maybe not all IT admins (namely helpdesk techs) need the capability to delete.
Already something that has been noted, while it hasn't been fully implemented you can see that this functionality is being built in with the admin module in terms of group permissions settings. So yep this will be covered (and very soon).