I do not think they should look back and "copy" things from singleplayer Final Fantasy games. However, when you play FFXIV you get the feeling this is their first and only MMORPG. They completely forgot everything they did in FFXI and started from 0 instead of taking the good parts of FFXI and implement them into FFXIV.

Some example
A search function to find player around the world.
An delivery/mailbox system.
An easier to understand and an easier to use create party system.
Map notes.
Camera system (including not being able to assign the arrow keys to anything in FFXIV).

Those things above are just a few examples. All of the things I mentioned above are important details that can make or break a game. However, none of those details needs to be unique in every single game. I am sure none would have whined about having the same /sea function as in FFXI or having the same delivery system as in FFXI or even have an action house like in FFXI.

To have a more direct answer on your question. No, I do not think all the answers for FFXI lie in the other FF games. They should look at FFXI a bit more and copy the good working parts of that game into FFXI. Not the whole gameplay, but simply things like a /sea function, party create function and so on. You summed up the other FF things pretty well (Cid, Chocobo, Airship, even Moogles). Those are things that are in every FF and they are in FFXIV too.

The thing I miss most right now is the thrill I had when I started FFXI. I miss the missions, the quests, the whole conquest feeling. If they would just copy that part from FFXI, but give it a FFXIV feel it would be good enough for me for the time being.

Maybe it will come, who knows. After all FFXI was out for a while before the NA release arrived (I am from EU but got the NA release myself). The last patch made me start playing again, but I would lie if I wouldn't say that I was stil la bit disappointed, especially at the new quests ....