Theatres are indeed good buildings, but only if you need them. And the only time i usually really need theatres is when i'm drafting.... so it comes down to GT->drafting again for me.
Btw, the difference between Great Lib and GT is that Great Lib actually does something for you, while GT won't do anything useful unless you're drafting - at least as far as i'm concerned. And even if it might be useful to build Great Lib without marble, there at least is a chance for +100% hammers on that building, a luxury you won't have for GT.
The greatest problem for me is that you can't do anything else with the city that builds the GT for a loooong time. It just takes too long to build and also takes a long time to pay back.
Edit because of crosspost:
You'll always have some culture pressure in border-cities with friendly neighbours you do not want to / can conquer in near time. Those cities need theaters for
Hm, rarely if ever happens to me. The only reason for me to build theatres is when i need borderpops and have angry citizens to whip in newly conquered cities, and when i draft ofc. But okay, i can see your point, although i fail to see the argument for GT in it.
You conquer other cities, those have the "we yearn to join our motherland" , those cities also need theaters.
They need to be whipped down, they certainly don't need theatres. And even if they do, just whip them.
Globe Theater isn't that expensive, it's only twice as expensive as Oracle, and it comes a lot later when production already is way higher, therefor, it's no big deal to build it.
But it comes at a time when you've plenty of good stuff to build beside a happyness building for happyness you actually don't need (unless drafting). Courthouses, AP buildings, Forges, Baracks/Stables to prepare your outbrake, Libraries and Universities to prepare Oxford, wonders for failgold, some soon-to-be-obsolete units for upgrading, or even wealth/research.
If i find myself in a position where i want GT, i usually build it in a city that has pretty much nothing else but alot of food. This also means: little hammers. So, it takes even longer ~ And if i whip the GT, i lose alot of precious population that could've been used for thousands of things.
tl;dr: it's not too expensive, but it just comes at a very bad time
One almost never has to research Drama onesself as AI techs it really well. Anyhow, even if one would have too, it's a cheap tech that can be awesome tradegood and speeds up Music which is a desirable tech because of the free GA.
Can't find an argument for GT here. Apply that argument to Aesthetics and you'll always find yourself Statue of Zeus because Aesthetics has great trade value (??!).
The Globe is just an awesomly powerful national Wonder, just like the HE, or the NE, don't you build those too? It's a little bit more expensive, but not much, and not keeping the argumentation above in mind.
Comparing GT to HE and NE really is way out of line. HE+NE are easily the two most powerful NWs there are, GT doesn't even come close to it - i'd set it on par with Moia statues at best, although i build Moia alot more than GT.
Long story short: GT only when you plan to draft. I'd really love to be convinced otherwise, but haven't read any rock solid argument for GT+Whip-only so far.
Even with Slider, my BPT / GPT are normally lower than without. I do not even ever had any problems with War Wariness, I'm guessing that you're simply loosing too many units.
It's the production that matters. If your HE suffers from +4 unhappiness and can't produce 1 unit per turn, you're certainly better off raising the slider. When your satelite cities won't grow anymore because they're unhappy, you're losing even more production. With a Bureaucracy capital, you might not lose commerce, but you'll lose tons and tons of production. That's what the slider is for from my pov.