While I disagree with some of your points, for example the little perks for each civ do change up the playstyle, they are not enforced changes. For example Songhai gets free temples and puppet cities will build temples whereas you cannot buy faith buildings in puppet cities.
Why is that relevant? Well you can gain happiness via faith from temples so you could, as Songhai, have a large puppet empire that isn't costing you much (because puppet cities lolbuildeverythinglol) whereas for most leaders you wouldn't want a large puppet empire. So Songhai can play a powerful culture game in a unique way.
Or you can just see 'free temples' and think nothing more of it. That is the beauty of Civ5, how best to exploit everything but not being a dead fish if you either don't want too or don't think of a way how too.
My second suggestion is to fight other human players. You can add me on Steam for games or just hit the lobby and join games but humans will offer hours of replayablity (give or take your tolerance) and their own playstyles may help you find creative things to do or ways to play.
As a singleplayer game, Civ5 with expansions did well for itself. I enjoyed it more than it's competitors at the time. I don't think Civ:BE will reach that point because of the 'build your own story' theme simply because their is no incentive to pick a 'suboptimal' setup except to challenge yourself or because you don't know any better, or put it another way, if Civ5 had the same setup option that Civ:BE does, would anyone honestly pick some of the perks like -25% tile purchase cost when you have so many better options to pick from?