That'd be the idea, but I don't think it'd work in practice because people would do exactly as you said. That's why I said I can't see it even being possible to implement unless you wanted to be way too restrictive like not allowing tickets to be abandoned. I can't think of a practical way to implement it. I'm just saying that, in theory, I think it'd be a way better system.
It would increase the number of unique teams able to complete the ticket. I think that would encourage more play (and thus, active searching and grouping) from average to decent players who would have a better shot at a perfect ticket.
And regardless, I can't imagine Bungie envisioned the event being riddled with sherpas. Maybe they did, but I think it kind of defeats the purpose of the event when repeated carrying is so common.