We can agree that concert tour with more GM later is better than using the same GM to theme Broadway. What I'm getting at is there a case where building Broadway will reduce win turn? Remember that it does take time to generate GM if you decide to generate them after a certain threshold tpt, let's say after you reached information era. For best result, you would start spawn them after Internet/NVC but maybe before airport. It takes around 26 turns to spawn the first 3 GM. You get benefit from higher tourism earlier from Broadway, and if you can win the game before the 26 turns, then your calculation for maximum TPT from musician doesn't necessarily apply. So I think the turn time difference will be based on how much roughly how much culture from AI you need to overcome.
It takes less than 20 turns to generate 2 Great Musicians (the 3rd one actually costs as the previous two combined), and with two Concert Tours you leap forward 20 turns (regarding Tourism), and win. So in this case, unless there were two AIs that were equally ahead in front of you (by ~20 turns) you would win faster.
I think there is no point in including CV wins without performing any Concert Tours in the discussion. IMO if you win a CV without performing any Concert Tour, you could have definitely won faster with at least a concert tour. So yes you have earlier tourism from Broadway, but if you are 20-30 turns away from winning, that is worthless.
Let's assume your maximum TpT is 1k (assuming WR, internet, broadcast tower bonus, ignoring OB, diplomats, TR, religion) and 34 from Broadway which is modified by +184% (50%WR, 100% internet, 34% broadcast tower) that gives 96.56 from Broadway wonder itself. We can just round it to approximately 1.1k tpt with Broadway.
I don't know how you got 34 TPT from Broadway before the % modifiers. You have 3 great work slots, that is 2 TPT base yield for each GWoM, another 1 from Hotel, 1 from Airport and 2 from NVC. The theming bonus it 3, but with the Aesthetics finisher that becomes 6. So before applying any % modifier the base is 24 (6*3 + 6), am I missing something? In the initial calculation I did not factor any bonus from ideology or internet so with a +148% modifier it still is ~60 TPT.
For example, for a 70k AI culture leader, you will need 7 GM in both cases. In this case, the tourism over time from Broadway would reduce about 3k tourism needed, but still wouldn't reduce the number of GM needed to influence him. Therefore Broadway is a net loss in this scenario since you'll need longer to generate the 7 GM than if you used them to theme. On average you'll buy 2-3 GM, so that still leaves at least 4 that has to be naturally born and victory depends on how fast you can spawn them.
Yes, in this example the tourism from Broadway is actually wasted, because you still need to burn 7 GMs, and you will end up with way more tourism than you needed. But this is an extreme case.
On the other extreme, for a 20k AI culture leader, but you only needed 2 GM and faith can buy them. In this case the Broadway would actually reduce the amount needed by about 4k. Also in this extreme case you don't need any natural GM.
Somewhere in between, there should be a break even point.
In the second scenario, if you only needed 20k to overcome why not spawn 4 GMs at 500 TPT and win faster? If you get 2 from faith then you just need to time the musicians guild and spawn the 2 GMs when you want them. There is no break even point simply because of this. Even in this extreme, when you will only need a small amount of tourism and the faith bought GMs are all that is needed, you could have timed Musicians Guild better and won faster.
This is why, for me, the CV is the most difficult. You need to time a lot of things, so you can get ahead. By performing a concert tour, you gain more than 10 turns for your win time, because a concert tour also means 10 less turns for the AI to accumulate culture. And this is significantly important once landmarks come into play.
For Broadway to be worth theming, the game would need to be a lot longer, but because as the game progresses AI will still accumulate culture, and it's CPT will increase, you need to also increase your TPT, so in reality the Broadway is not worth it because in a CV you want to win as soon as possible, before the AI will start accumulating huge amounts of culture. So the only time to build Broadway would be when you would actually use that "free" GM to perform a concert tour, but Broadway comes too early for that.
Also if your tpt isn't 1k, but only 500, then the calculation favors Broadway more when it accounts for 20% of your total tourism.
Yes, that is why I chose 500, to further prove that theming Broadway is not worth it for CV.
Also regarding Eiffel Tower, Eiffel tower has higher tourism at the time it is build, so it's definitely priority, but usually you can build both if you plan to get Broadway anyway especially if you're used Oxford for Radio.
This discussion was for a non-CV play, when you just want tourism to counter ideology pressure, and you only need to pick one. If you can have them both, that is better, but personally I'd rather take Eiffel Tower and then focus on the ideology wonder. If you have a lot of faith you could use GEs on them, but if by doing this you lose GSs it's not worth it.