The disadvantage of ONE person handling a ticket is that only ONE person is involved, and when they end their shift and go home for the day/night or worse, take their 2 days off, then the ticket goes unanswered as it's assigned to a specific operator.
Having multiple people work on a ticket (especially since everything in the issue is being documented in the ticket) is that the client gets the fastest possible answer from whatever staff is online and available to answer the issue.
I can't tell you how frustrated I get with eNom and other places where my ticket is assigned to a person, and I have to wait for them to come back on shift, or come back after the weekend so I can get a response. I'm all for assigned representatives etc, but if that person is not available, I shouldn't be forced to wait for them to come on staff. Any able body personal with answers to a question should be answering the question.
At least that's how we've operated, and clients seem to be more than pleased with their results. When specific staff members are requested, tickets are assigned to them, but beyond that, the primary mission for our staff is to answer tickets as quickly and accurately so that the client can resolve the issue and close out the ticket once resolved.