I think people underestimate the sacrifice of forgoing mines on most of your hills. Using the rough-hewn church will basically cut your production in half across your empire, and if you don't save forests/rainforests until you can make lumber mills on them - which really happens too late to suffice, and you'd have to forgo chops - production might be so low that your cities aren't really functional at all. You really need a certain benchmark of production in order to play the game.
What few mines you might get from the church's adjacency restriction will not be enough. Keep in mind that you also pretty much have to settle on a hill, so that's another mine gone already. This will cripple nearly any city barring those with wildly improbable terrain, like 15 hills or a natural wonder that improves production surrounded by woods. Your typical city will have, what, maybe four hills? If you give up three of those for churches, that city will be stuck at like 12 production forever.
I think this improvement will end up being like the Incan terrace farm: you might make one or two in choice locations but you can't put them everywhere or you're irrelevant by turn 100, and in the end it means that the improvement just doesn't have that much of an impact. I don't see how you can realistically expect to make more than one or two of these in an average city without turning that city into complete trash. Like the Mayans, this civ gives me the sense that it's good if you're willing to restart six times to get suitable land but crippled by its design if you don't do that.
At least Ethiopia doesn't have built-in penalties, but I predict that its bonuses will not be nearly as good as people seem to expect. Have you tried playing civ with a self-imposed "I don't make mines" rule? It's nearly unplayable. Someone who normally plays Deity would struggle to win on King. Production is the most important yield by such a distance that sacrificing significant amounts of it is just not an option at all.