"Urgent" and a debate of 24 hours vs two business days do not belong in the same discussion.  If something is urgent, it needs to be dealt with immediately.

There are two distinct and separable issues intertwined here, authorization to make urgent requests vs making an urgent request.

If someone is authorized to make an urgent request, the request should be processed and responded to within seconds.  The processing should be completely automated.

The sticking point here is authorization.  Let me suggest three cases.
  1. The requester is a member of a recognized group, e.g. an appropriate law enforcement agency.  Everyone in that group is authorized.  Requests for urgent responses can come from any member of that group.  This presumes there is a method for the requester to present appropriate credentials.  Repeating the above, such requests should be processed automatically, with a response time measured in seconds.

  2. The requester is not part of an authorized group, but has received individual authorization.  This is essentially the same as (1) except the authorization is to the individual and not to a group.  Again, the request should be processed automatically.

  3. The requester has not been authorized in advance but feels it is necessary to get registration urgently. It's this sort of request that will require human intervention.

    I would guess that this sort of one-off urgent request would be relatively rare.  Moreover, it would be fairly expensive for the registrars to be always ready to respond to such requests on very short notice.  Two business days seems ok to me.

    That said, an alternative path for the requester is to find  an authorized person who is willing to make the request on his behalf.
Steve