As Sleepless noted, the third city will (hopefully) be mostly culture bombed. Culture bombs don't get any benefit from Cathedrals.
What is our reason for picking Kyoto? I suspect it is the high
the city can generate, and it has a few cottages already built which are a bonus. The problem is, if it can't reclaim the tiles east of the city it is actually kind of lame.
Does everyone understand how tile culture works?
Culture Mechanics Disassembled.
It's a pretty long read, but in summary, Kyoto isn't just competing with the culture generated by the nearest overlapping Japanese city - we are actually competing with that city + all the culture that Kyoto ever produced back when it was Japanese.
We're now at turn 135. Imagine a tile 1E of Kyoto.
Kyoto started the game with a palace + castle + religion for 4cpt. In the first 3 turns the tile 1E has 12 'plot' culture.
Once Kyoto's borders expand, the tile gets a bonus 20 cpt. After the next 22 turns the plot will have 22*24+12 = 540.
Then the borders expand again. The plot now gets a bonus 40 cpt. Best case scenario, the city never built any monuments or temples, so stayed at 4 cpt. 100 turns later the city will have 100*44 + 540 = 4,940 plot culture.
I think it's safe to say we need to overcome anywhere between 5,000 and 6,000 culture to reclaim the tiles 1E of Kyoto. Even if we're producing 60 plot culture per turn (base of 20 + 2 border expansions for bonus of 40) it will still take over 83 turns for us to reclaim the tiles naturally.
This is where a GArtist bomb comes in.
Suppose a great artist creates a great work in a city that has no culture. The first of the 200 point groups of culture is added. This brings the city's culture level immediately up to 3. Now, although a turn worth of the city's culture is now delivered, the city has no culture and is producing no culture. So, the only plot culture gained is from those 20 point bonuses. The city plot and 8 surrounding squares thus get 40 points of plot culture. The next ring gets only 20 points in each square. Now, we repeat. The next 200 points is added. City's cultural level stays at 3. Same amount added to nearby squares. Third 200 points added. This brings the city's cultural level to 4, where it will stay for the remainder of the cultural delivery as we're only giving 4000 points and it needs 5000 for the next level. So, the innermost ring gets 60 culture each of 18 times, the next ring gets 40 culture 18 times, and the third ring gets 20 culture 18 times. Or, to sum it up, The first ring gets 1160 points of plot culture, the second ring gets 760, the third ring gets 360 and the fourth ring, although within the city's cultural radius gets nothing. This may seem like a lot, but consider if you sat on the city for a mere 20 turns, you'd double it. Of course, if the city also had any cultural production, that amount would be delivered 20 times to every square in the first 3 rings, and 18 times to the fourth ring.
Note that when the city's culture is delivered, it is the amount that the city produces at that instant, not that turn. This should raise some mental red flags as possibly abusive, because yes, you can set your culture slider to 100, assign everyone to artist specialist, deliver your culture bomb, then set them back before ending your turn. Knowing this, you can get a great deal of benefit at no cost, if you know the trick. Well, actually, there is some cost, because to use this trick to say add another 1000 to all your squares' culture, you'd need first need to build the city up to where it can produce 50 CPT.
In Kyoto's case we won't be starting from scratch, but from the 2nd or 3rd rings already. The tiles 1E of Kyoto would receive 20*60 = 1200, 2E would receive 20*40 = 800. However, we also get 20 turns worth of the current culture output. Assign 10+ pop as Sistine artists (60), culture from buildings (~12), maybe a temporary 100% culture slider (~10) giving a total of ~82. This puts or total plot culture in the tile 1E at 1200 + 82*20 = 2840.
(It can be even better of we've built a Cathedral or two)
The problem here is that that still might not be enough to reclaim control of those tiles (without cathedrals). We would need at least 2 GArtist bombs to reclaim the tiles. I should point out, that this is actually entirely feasible
At least we get 'extra' value out of the GArtist bombs, since for a typical cultural game the only thing you'd really gain is the city culture. In our case, we also appreciate the plot culture.
So, that's one problem with Kyoto.
Another problem is that it is also our line of defence for the eastern front. If we are attacked, we really can't afford to lose a legendary city.