They also got the age setting wrong, it was more modern that the previous games, but it didn't advance enough, or any. I mean, playing as a prehistoric village that manages to become the Roman Empire is satisfying, but playing as British citizens that try to conquest North America... and that's it, isn't that exciting.
The more sensible approach would have been do a "Empire Earth" game. Starting with prehistoric men and ending with intergalactical civilizations.
This, so much this.
AoE 3 had innovative gameplay mechanics but the historical time period between the 16th century and the Industrial Age simply wasn't interesting. And I didn't want to freaking colonize America, give me something epic! And the SP campaign that depicted the history of the fictional Black family was far from epic (not that SP matters that much for an RTS).
The Ancient times and Medieval times just are so much much more interesting settings than the era between 1500-1850, from a historical and mythological perspective, at least in the context of a game.
And swords-archers-siege is much more exciting than guns and cannons.
Clearly they should have tried an Empire Earth approach or just chosen a different epoch no matter if it had ruined the chronological order.
So that's what went wrong. Age of Empires 3 failed. Actually it already started with AoM, because they chose bad timing to go off the historical path and it fractured the player base. And only 3 civs in AoM, WTF was that? AoE2 was dearly loved not least because it had so many civs.