For me, economic depth is not "I need to remember to build a Lumber Camp when my villagers are walking more than 3 tiles to get wood." I understand that such decisions can help separate out more skilled from less skilled players, but they don't feel like strategy to me. *
Instead, economic depth (again, for me) is deciding whether or not to hunt outside of your base or to farm inside your base. Farming is slower but safer. If you get attacked when hunting, you may be in trouble. But if you are farming and the enemy is hunting, you'll have fewer resources. Think about all the decisions that can fall out of this fairly simple difference in gathering:
-- Should I build towers out to protect my hunters?
-- Should I get hunting upgrades knowing that I may flee inside my base before long?
-- Should I concentrate on units that don't cost much Food, knowing that my hunters may be in jeopardy?
-- Should I scout my enemy to see if he is hunting?
-- Should I hunt far away from my town, in hopes that I'll still have hunting near my town later?
-- Should I hunt near my ally, knowing that we'll run out of Food faster, but have safety in numbers?
-- Should I attack my enemy quickly, forcing him into his town, and leaving all the hunting to me?
-- Should I put excess gatherers on hunting early, since I may not be able to hunt all game?
Now imagine that you add 2-3 more ways to earn Food, and suddenly you have a lot of depth. The same strategy won't work against every player on every map in every situation. If we really wanted to dumb down the economy, we'd make sure there was a "right way" to gather Food that worked in 99% of cases (or just get rid of multiple ways to gather Food altogether).
* - One of the designers here jokingly proposed the "Apply Bandage" button on every unit. Then, when you're in a fight, you frantically mash the "Apply Bandage" button to keep your units from bleeding to death. The player who can mash the button faster will likely win the battle.