They only take two flatland tiles for whopping 7 culture each. That's easily 14 culture per city, which is quite adequate for a space race.
How do you manage to get 2 Bateys at 7 Culture per city easily and consistently? Seriously.
I believe that the Bateys are underrated*, since putting an Entertainment Complex next to a Bonus resources can give you 2 Bateys at 5 Culture each easily
(with the Exploration civic). You can also sneak a Batey between 2 Bonus resources for 3 Culture in the early game, then build the Entertainment Complex afterward for 4 Culture that will become 7 Culture once Exploration is unlocked. But I don't believe you can achieve an average of 7 Culture per Batey across your empire.
* : I believe many players underrate global yields (culture, faith, gold, science), miscalculate passive yields (housing, amenity tourism, power) but overvalue local yields (food especially, production is king though). A Batey at +5 Culture feels as 4 yield since you can only put it on flat tiles and have to compete to a Mine at +3 Production that feels as 4-5 yields because of the hills / resources / both.
It also come on when you discover the City-State and became the Suzerain. You cannot plan the game on having a specific City-State being on the game to fulfill your Culture plan. Since the Batey needs you to plan around it, being aware of its existence only late in the game means you miss on several opportunities. It is the same problem on late unique improvement like the Château, where you need a second Builder wave in order to remove / rebuild tiles accordingly.
I understand more your point. But it is specific to overly densely packed civilizations that happens to have few tiles and Population meaning each Population has to work meaningful tiles, yet not harvesting the Bonus resources to free space for districts, and putting Entertainment Complex in all city for the +3 Amenity. I don't believe that is a common play! Mostly the Entertainment Complex spam!
More seriously, you like the Batey more because it synergies well with your way of playing. All the cumulative pocket Culture become consequent toward climbing the Civic tree, while you do not care about the Tourism. The Moai has a different use: it is greater for its spammable purpose and Tourism at flight. You can achieve a higher sum of Culture to convert at Flight than the Batey could do. You could even settle a ghost-city in the middle of the snow that will have no other purpose than having all tiles being Moai. The Moai is just more flexible and need less planning to achieve good value.
In short: I agree with you. The Batey is strong, but need planning in order to achieve high Culture. It also depends on how you play the game: the Batey synergies better when you cannot dedicate many tiles while having a lot of Entertainment Complex. But you can plan around the Batey only if you know the City-State is in the game early on. Furthermore, your gameplan or the victory shouldn't rely on the existence of a specific City-State in order to cover a hole in your strategy, because it means that strategy is flawed from the start. In the end, even if the Batey is strong, players do not expect to count on it in order to increase their Culture output, and might go for suzerainty of another city-state instead (since they need less Culture, the Batey become less valuable).