Whilst I haven( played Halo Wars yet, I've played over 1500 hours of single-player AoEII between HD and DE editions.
The main reasons why mouse is important:
1) AoE2 is a macro-heavy game. This means you are both managing resource collection and base building/advancing AND combat, usually in different parts of the map.
2) Age games are based on counters and hidden bonuses- a pikeman does +32 bonus damage to cavalry units, for example, but also takes bonus damage from certain ranged units. So the micro really comes from selecting the correct unit type out of the scrum (with double-click) and making it sure it attacks the units it's strong against, instead of something that has extra resistance against it. AoE is literally all about taking smart exchanges. And this requires precise, immediate controls. Unlike many RTS games, such as C&C and StarCraft, there are no "ultimate units"- you can't just build 20 Mammoth tanks or BattleCruisers and attack ground in enemy base and watch them wreck everything- only a few civs have such "deathball" combos, and even then, they require several units- usually siege with infantry, and some cavalry to watch the flanks- and these units STILL need to be microed to disengage from dis-advantageous fights.
These aspects of AoE would be difficult to replicate on a controller, imo. If the game revolves around map control and making simultaneous decisions in several parts of the map, then controllers just can't keep up, because using the mouse to click on the mini-map is the ultimate convenience, even if you are not using hotkeys.