[Manwe Sulimo]

Why do I say that going down Anduin would've resulted in the detruction of the Human Kingdoms? A number of reasons:

1) The time taken going first east, then south, would've spent more time than Rohan had. The Uruk-hai would've attacked and destroyed Helm's Deep (without Merry and Pippin the Huorns never would've been drawn/sent to Helm's Deep), the Ents never would've attacked Isengard, and after that, Edoras goes.
2) Gandalf would not have been killed, meaning that Gandalf the Grey would've remained. He would not have had the power to defeat Saruman (by breaking his staff, for the reason that he wouldn't have been able to enter Isengard [see reason 1]). Also, he would not have been able to organize the defense of Minas Tirith as effectively, and would not have been able to face down the Lord of the Nazzies at the Gate.
3) The Balrog never would've been killed, giving Sauron/Saruman an effective weapon against Lórien and Rivendell.
4) Éowyn would not have survived/been made a slave, meaning that the Witch-king would not have been killed.
5) The Rohirrim would not have been able to help Minas Tirith.
6) Aragorn would not have been able to travel the [BUM BUM BUM] Paths of the Dead ("Neigh") and, consequently, would not have been able to liberate Pelargir.

The story with Gundabad:

The Elrond was sure that the pass near there was infested by orcs/goblins/troll. They were not sure about Moria, and besides, they were planning on using Caradhras.