Hindsight is always 20:20. Thing is much of the Fellowship's plans got changed - Sauron's betrayal changed much of the landscape and put an enemy at the Fellowship's rear and far further into the lands that should have been more peaceful. Even before the Fellowship broke its clear that Gandalf needed an excuse to separate the Ring from at least the human companions. So a split was always going to be on the cards at some stage. If anything the only major risk was the Frodo wouldn't find a way into Morder - indeed he only chanced on that by virtue of Gollum. Without him Frodo would likely have had to try and get through the Black Gate (and remember he can't just put the ring on that close to Mordor).