It would be much easier and cause less impact to create a new TLD, say ".nonprofit",
or something along those lines. Not all "organizations" are non-profit or not-for-profit.
When Jon Postel suggested that ".org" should be used for non-profit organizations,
he had no way of knowing that new TLD's would be added to the system.
That way
the rules could be determined before the names are put into use. There would be no
need for a compromise, as would be the case if they chenged the rules on ".org".
As a business owner, I have some domains at .org TLD because my business is an organization.