Why Moria?

[Tuor of Gondolin]

If you're starting in the Shire, yes. If you're starting at Rivendell- which is whether the decision to destroy the Ring was made, then it's about as far back to the Grey Havens as it is down to Rohan, and Rohan to Mordor is about the same as Belfalas to Mordor- so even a fast sea voyage means needless extra time if you're starting in Rivendell.

Ah, but sailing from the Grey Havens assumes they leave
Rivendell immediately after the Council, without waiting
some months. Plus going by sea avoids going over the
Misty Mountains in winter and/or past Orthanc.