Here's a few things I would like to see the AI being capable of doing in FE
1) The AI should form alliances based on logical (we need to combine armies because Umbar is too big!) and illogical (I happen to love earth shards, and you have one, so I have to take it from you!) scenarios. These alliances should be built so that the AI is both capable of supporting its allies, and at the same time being ready for backstabs and being capable of abruptly ending alliances with "allies" that happen to overextend. The AI should continuously deal on a diplomatic level with other AI factions, in order to prevent the player from steamrolling, or supporting the player if he is being steamrolled. Similarly, the AI should react to the reactions of AI players - if one AI attempts to forge an alliance with the player, another AI might sell them diplomatic capital or materials to prevent that from happening.
2) The AI should design units that are primarily aimed at defeating the enemy they are currently most threatened by. Derek has shown us small glimpses of the depth of weaponry and armor, and there have been numerous hints about traits and such. These should be used for tailor-made units that are particularly proficient at defeating the most important enemy. If they've got castles, you build units that can overcome walls. If they've got lots of magic, you build units with high magic resistance and life. If they've got a lot of archers, you build units with shields and mounts. If they're Capitar, you build units that hate capitar (if that's a thing).
3) The AI is profoundly efficient with its use of spells and mana, primarily on a strategic level. Derek has shown us the spell list, of which at least half are happening in the strategic map. The AI should be able to balance each of these spells against each other, to
a) prevent shortcomings in its own industry, and adapt spells chosen to its current situation. If we're at war, or we need units quick, we boost our weapons or summon elementals. If we're at peace, such things should be dispelled, and the focus should instead be on production value
b ) prevent blitzkrieg advances from the player, by teleporting units around or raising mountains to prevent the enemy coming close to your city, or causing an earthquake that forces them to stop for a turn
c ) support, and indeed LEAD any offensives that the AI decide to mount against enemies
4) The AI should have diverse paths from which it advances in tech trees, city construction and champion design.
5) The AI should be showing off a controlled randomness in its diplomatic nature, instead of calculated risk down to the last decimal. Features that serve to define one AI from another in the same game, should be randomized almost completely each game. For example, Pariden might always love magic (it was their thing in E:wom) but in one game they might build an army of knights, and another they'll focus on recruiting monsters from the wilds instead. In one game they might go for a diplomatic victory by forming alliances and weening out the offenders, in another game they might be trying to strongarm everybody. In one game they might be very forgiving for attacks you've performed, in another game even touching them once will cause a permanent war. In one game, Pariden might focus almost completely on strategic spells, in another its all tactical spells. How the AI feels and acts should be represented in its conversations with the player.
Perhaps a bit overreaching, but this is a wish list!