This seems like as good a place as any to make a first post.
10. Remove reclassing. The only time I ever used it was on my avatar, and even then it was only because his personality showed little to no affinity for any one class.
9. Return to more realistic armor and weapons. I liked the more realistic equipment of older games it just made Fire Emblem look a little more distinct.
8. Automatic class upgrades. It felt a lot better to have a unit automatically upgrade at level 20 in Sacred Stones. Better than having to search for a master seal in Awakening at least.
7. The magic triangle. It was cool, cool things are good, good things should be in Fire Emblem.
6. A customizable unit with more mechanical, and personality customization. The asset/flaw system was nice early game, but mid-game stopped being meaningful at all. An expanded system for customizing your unit on mechanical level would be lovely. Dialogue trees are always a great way to customize your character's personality, so that'd be nice.
5. No genderlocked classes. I know that this is an unpopular opinion, but I've never seen the need for genderlocking in any game. Unless the classes were named the womancer or the manzerker, but I doubt those will be classes in Fire Emblem.
4. Third tier classes. I've never actually played a fire emblem with tier 3s, but they sound awesome.
3. Better story. Reasoning is the same as #7.
2. Better supports. Awakening supports felt awkward with it's weird "Just friends, just friends, just friends, BAM! MARRIED!" system.
1. Meaningful story choices. See #3 and #7.
EDIT: Just remembered two things that I couldn't remember earlier, so I rolled all the customization stuff into one, and added them in.