Although it would have been a fascinating idea, I think that using the building of the Federation alone as the main storyline would have been very hard to render without a common thread. After all, having Vulcans, Andorans and Humans just interacting with each other episode after episode without any underlying plot could have become boring (and a bit sitcomish as well - like the characters who keep bickering at each other but about whom everybody knows that they will become friends in the end).
Of course, they could have used the Romulan war, but for once, that one would have been very hard to show while staying in canon : ships battling each others with nuclear warheads without even seeing one another...
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett