Great set of posts
To add something to the discussion, I am surprised that Heroes of Might and Magic has not been mentioned as it is the closest type of game to this one (either III, V, or VI). It has tactical battles and is multi-player. I have played a few games of all three in mulit-player and I have to say it was not a good experience in any of them.
This is because of the tatical battles of course. If you play with more than two people, then whenever two people fought, everyone else had to wait around and do nothing until they were done. Given the number of battles in Heroes, this got old pretty quick.
The solution that was implemented (in V I think) is that the people whose turn it was got to play in what was called 'ghost' mode where they could move around the map in limited fashion. Needless to say, this did not do much to help the wait time while the tatacial battles were going on.
While the battles could be auto resolved, in pratice, this was not done because the losses from the AI running things were generally much higher than if run by a person. As auto-resolve was an option on a per battle basis, the players who used this a lot were at a disadvantage to those that did not. So this had the effect that 90% of all the battles (including those against netural forces) were all run by a person versus using the auto-resolve function in order to stay at a par with everyone else.
So to solve the issue with a strategy game like FE with tactical battles would be required to either auto-resolve ALL tatical battles to have all the human players have the same type of losses or find some creative way that people not involved in a tatical battle have someting they can do while waiting for others to finish. Or maybe a completely new tatical system that no one has thought of yet
I do play a lot of the CIV series MP (III, IV, and V) and even that has issues with waiting on others to finish their turn, especially if they have a large empire. However, as there are no tatical battles in Civ, the wait time is still much less than it is in Heroes. So it is more toleable. Especially since you can still look around at your stuff and plan out the next turns. Plus, if you really want to move the game along, you can set a time limit/move and when the time runs out you are done and the next turn begins. This makes the possible wait time even more managable.
Once last example, Total War Empire. You cannot play MP in the strategic mode (at least I could not the last time when I played it a long time ago). Only the tatical battles were MP. To me that sucked as I wanted it all So I never bothered as I wanted the tatical battles to mean someting in a larger context.
The MP games that I hve found work the best (at least imho) are all real time games. These are like Age of Whatever (fill in with whatever version you want lol), Hearts of Iron series, etc. and pretty much any turn based game that has simultainous turns AND no tatical battles. This is because for many MPs like myself it is the wait time between that is the killer.
If FE can manage the wait time between turns in MP by some reasonable method that retains the flavor of the game, then MP inclusion makes sense. If that is too costly, too hard, etc., then MP does not make sense. To me it really is that simple.