Tim4Fun has inspire me to say what is important for FE.  I've said mine, what is yours?! I am trying to just talk about the big picture here!

If FE can do all of the following, it will be a classic fantasy TBS game, that I play for years to come!

1) The 'sphincter factor' was always present: It seems to be a combination of unknowns, risk to your main city/sovereign/production, and things which cause you to significantly change your strategy (world enchantments, random events, strong roaming monster/wildland civilization that diplomacy has little effect, opponents is reaching victory). Gamer is always sitting-on-the-edge that expect challenge is always around the bend, and has some time/way to counter it, from 1st to 1000 turn.

2) Large variety of cool & powerful combinations: Like, I could cast flying on my slingers. Or I could buff my fighter with a lot of different spells and tools. I could put a Loxodon warhammer on my Vault Skirge...

Yet, AI player knows how to counter them one way or another. Even better, AI knows how to use combos too.

No combo is perfect. There is always opportunity cost, or weakness somewhere for the combo. Make specialization has a cost, make generalization has a cost.

3) So, gamer will start a game wanting to test this combo or combo a combo with another. Test them in a variety of map configuration, made by a well tuned RMG.

4) Streamline away any non-decision making related 'wait' and 'mouse-click': And, micromanagement was somehow balanced to an acceptable degree. No silly waiting for 5 seconds sword swing animation to end, nor long wait for the AI player etc (e.g. use WE-GO tactical combat). Avoid repeatness, tediousness.

5) Have really different styles of play 

6) Early units/building/technology does not become automatically become obsolete in late game. Design them in a way that further investment on them will yield a reasonable result/effectiveness even in late game. Late game stuff is always better. However, disbanding what you've already invested/build is not always wise.

7) Give us mechanism so that we do not need to do the following every game:
a. Getting the most population by spawning big cities/building, because pop -> production -> fire power to kill everything = win.
b. Combat does not just comes down to who get the numbers, in late game. No matter in early or late game,  skill/tactics/good troop composition is always a decisive factor.  

Rock/scissor/paper works in any stage of game,  for example, a holy warrior can always slaughter 10X amount of undead (cost-wise) no matter how low end this particular warrior is.    And for this low end warrior, any highest end warrior can has a cost advantage of 5X.    Highest end holy warrior have 10X to 50X cost adv dealing with undead, depending.

8) Do not just give us new toys as the game progress.  Instead, give us very "distinctive feel" on different stages of game; while how you reach this feel depends on what you've done in previous stage.

9) Time-wise, make tactical combat occupy around 50% of the game. This is where we test our combos/tactics. Have some mechanism to allow us to skip unimportant combats. Some wise mechanism to control time for MP games.

10) Then, Some of my previous misc suggestions

What kind of FE you would like to play?