Absurdly Lacking MP Support
No improvements at all from CIV IV: No dedicated servers, no matchmaking, constant lag issue, framerate problems, no online ladder and rankings, no unit animation, random crashes, no way of reconnecting a game, no way of joining a mid-game through invite.
No reason to play MP at all.
No Civics
Civics was another extremely well-thought out feature that was added in CIV IV. Not only did it add flavors to each nation (Communism vs. Capitalism, Emancipation vs. Slavery, Universal Suffrage vs. Police State), it provides long term tactical options as well as short term flexibility to players to adapt their empires based on the current circumstance. Deciding and changing Civics was always a weighty decision because each one of them have their pros and cons. It makes each nation unique because rarely do two empires have the identical set of Civics.
In CIV 5 Civics are replaced by Social Policies, which is fundamentally a ladder of perks with bonuses that you can upgrade one at a time. It may still be strategic to decide on which branch of policies and perk to upgrade, but because of the fact that they are permanent and you cannot change them, they offer absolutely no tactical flexibility to players. All branches and perks add some kind of bonus to your empire with no negative side effects, so the decision of choosing which one to upgrade also becomes less significant.
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