Well, there's obviously a strategy difference between us—I always have Broadway and the Eiffel Tower before Hotels; you always go the other way (I use Oxford to pop Radio and jump into the Modern era early, getting a head start on the ideologies). Either way, you're talking about a strategy that relies entirely on Landmarks and doesn't generate enough Artifacts to fill Museums outside of core cities. Split the difference between your estimates—call it 20 Landmarks on a continent. Say the average era is Classical, you go Freedom (you probably won't have New Deal when you get to Hotels), you pass Historical Landmarks. 8 culture per Landmark, 4 tourism with a Hotel in every city—80 tourism altogether (120 when you get New Deal). In a tall game, maybe you only dig up half that many and stick them all in Museums etc. With hotels, you get 30 from the Artifacts themselves. Stick two in the Louvre and eight in your four Museums, you get another 24 from theming bonuses. Advantage: Landmarks—eventually. However, the Artifacts and theming bonuses are generating 44 Tourism per turn in the Industrial era; the Landmarks generate nothing until Refrigeration, and don't reach their full output until you've passed WC legislation and gotten a Tier 2 tenet (from a specific ideology). And this strategy requires you to conquer your entire continent and maintain tech parity with a 10+ city empire. It's certainly workable, but it's fairly narrowly applied.
I should amend what I said with two exceptions, though: if you get a great, faith-heavy religious start and can get multiple religious buildings up in every city in a wide empire, you might be able to win a cultural victory before Hotels even really come into play, especially if you can also stay on top of the culture/tourism Wonders. Also, if you finish Exploration late in the game, pivoting from tall to wide at the very end—to set up a bunch of little cities near hidden antiquity sites for Landmarks—would definitely help push you over the edge.
Edit: the above is @Roxlimn
No, my point was that, generally speaking (France, Polynesia, India, and Sacred Sites all being exceptions), you can only generate so much tourism in a given game, no matter how tall or wide you go. There is a fixed number of Great Works that can be created; there is a limited number of Artifacts/Landmarks that can be produced. Thus, there is a limit to how much you can gain by building more than ~4 cities, even setting aside the sacrifices you have to make (in terms of science, social policies, happiness, etc.) to build 5+ cities. Where Great Works and Artifacts are concerned, that limit is actually reached very, very quickly—I don't think you ever need to build more than four cities to have enough slots to house them, unless you go completely berserk with Archaeologists (which, I would argue, is counterproductive). Roxlimn outlined a strong strategy to go wide and make use of Landmarks, but, as I explained above, it's a fairly narrow strategy. Going tall will always produce good results, allowing you to pursue whichever policies and ideologies you like and not requiring you to go to war. Roxlimn's strategy may produce better results, but it requires specific policy and ideology choices and successful early conquest.
Similarly, this is a strong strategy with narrow applications. As Sadato acknowledges at the top of the OP, it's weaker at high difficulties—you're very unlikely to get more than one religious building at Immortal+, and you might not get Sacred Sites at all. You might be able to consistently apply it with Ethiopia, but a one-civ strategy is still a fairly narrow one. There are extremely effective wide strategies for tourism, but going tall is more reliable and generally stronger.
I should amend what I said with two exceptions, though: if you get a great, faith-heavy religious start and can get multiple religious buildings up in every city in a wide empire, you might be able to win a cultural victory before Hotels even really come into play, especially if you can also stay on top of the culture/tourism Wonders. Also, if you finish Exploration late in the game, pivoting from tall to wide at the very end—to set up a bunch of little cities near hidden antiquity sites for Landmarks—would definitely help push you over the edge.
Edit: the above is @Roxlimn
Wigwam,
The main thing missing from your analysis is that it is cumulative tourism and cumulative culture that determine if you reach influential with others civs. The fact that a wide strategy won't have as much tourism in its capital as a tall strategy by the time hotels roll around is offset by the fact that wide play can potentially have higher tourism accumulated before then. So wide play should be leading in total tourism for most of the game while tall play should really spike at the end.
No, my point was that, generally speaking (France, Polynesia, India, and Sacred Sites all being exceptions), you can only generate so much tourism in a given game, no matter how tall or wide you go. There is a fixed number of Great Works that can be created; there is a limited number of Artifacts/Landmarks that can be produced. Thus, there is a limit to how much you can gain by building more than ~4 cities, even setting aside the sacrifices you have to make (in terms of science, social policies, happiness, etc.) to build 5+ cities. Where Great Works and Artifacts are concerned, that limit is actually reached very, very quickly—I don't think you ever need to build more than four cities to have enough slots to house them, unless you go completely berserk with Archaeologists (which, I would argue, is counterproductive). Roxlimn outlined a strong strategy to go wide and make use of Landmarks, but, as I explained above, it's a fairly narrow strategy. Going tall will always produce good results, allowing you to pursue whichever policies and ideologies you like and not requiring you to go to war. Roxlimn's strategy may produce better results, but it requires specific policy and ideology choices and successful early conquest.
Similarly, this is a strong strategy with narrow applications. As Sadato acknowledges at the top of the OP, it's weaker at high difficulties—you're very unlikely to get more than one religious building at Immortal+, and you might not get Sacred Sites at all. You might be able to consistently apply it with Ethiopia, but a one-civ strategy is still a fairly narrow one. There are extremely effective wide strategies for tourism, but going tall is more reliable and generally stronger.