I don't quite see why the sistine chapel is so great for a cultural victory.
I'll try to explain a bit.
It only adds 2 culture per specialist and I won't use many specialists in a city that's going for the legendary culture level. A well developed cottage adds far more culture when at 100% culture. And that's the normal way to go for a culture victory (at least that's what I read in most of the posts on this forum and what I do myself).
That's exactly the point!
What is difficult about cultural wins?
It's having 3 legendary cities. The capital is usually easy to grow to legendary.
Then there is a high commerce city that will be founded early enough to have all those nice cultural buildings and mature cottages.
Then you can build another commerce city or a GPFarm.
You will need a GP farm, since the 3rd city will probably need some help (= GArtists) to not slow down the win.
If you go for sistin chapel, your GP farm will be your 3rd city.
If you let sistin chapel go, your GP farm will be another city.
I played a lot of cultural games, and I found it much easier to have
2 good commerce cities + GP Farm + helper cities than
3 good commerce cities + GP farm + helper cities.
When going cultural, it's not always easy to capture more cities. You want no enemies! So being able to make with 1 less great spot is huge.
With sistin chapel, your GP farm will be producing enough culture/turn to not slow you down. 6 artists + sistin chapel will be enough.
(+ every settled specialist (including GGenerals!) gives 2 cpt (before modifiers), this is just the icing on the cake)
Or do you go for a culture victory without the 100% culture slider? In that case, I understand. The rest of your cities can go on with their job at a normal science-gold rate while the 3 cities going for legendary culture just use specialists. But it will take a long time if you were playing at a level where you couldn't get many of the wonders of the world.
I'm not playing above monarch (except rome and incas

), but at monarch level I won without culture slider too.
By the way, I've only gone for a cultural victory once. I don't quite like the option.
Maybe you tried it in the most academic way? I find it boring, when I try to do it "just perfectly". I favour a more balanced game, where you spend less time in an obviously weak situation.
I can see the usefulness for capturing cities. That's a nice feature of the wonder. I hadn't thought about that before. I usually will build culture the first turn that a city comes out of its rebellion. For a small city, the 8 surrounding tiles can often be enough for a while until the first border expansion occurs. Sometimes, I will rush buy or pop rush some buildings in such a city.
Still building a great wonder just to get some marginal just captured cities up and running a few turns earlier is not that great in my opinion. But it does show that the wonder has its uses.
That was my point. This wonder has its uses.
You simply must see them

.
I agree that saving 2 pops (those you would sacrifice for the theatre) and losing 3 turns of expanded territory isn't much.
But this is a really common situation, something you might face 30 times in the game. So it's not totally marginal.
It's a lot less straightforward than the oracle of course, but shaving off 3 turns in every city can make domination a lot easier, and rushing a courthouse instead of the theater can help a lot too

.