Most often, however, the top teams use the same VC so why stipulate it? I don't get it.
A good portion of my reasoning delves into the area of strategic discussion. We're not supposed to have much strategic discussion in this thread, which is why I initially proposed the idea from another perspective. But, I'll try to lay out the concept by speaking as generally as possible about potential strategies while still describing my thought process.
Excluding an Espionage Cultural Victory, it's quite rare to see a Cultural Victory in SGOTM when it isn't stipulated. Yet, I think that SGOTM is where a lot of solid discussion and strategies arise, and it would be nice to see this Victory Condition better explored (as WastinTime and Fippy had suggested).
What I think makes a Cultural Victory partner particularly well with this game is that some of the traditional approaches to a Cultural Victory, such as spamming a ton of Wonders on lower-to-mid Difficulty Levels or such as taking over the world (like with most other Victory Conditions) then using all of those resources to power your way to victory don't apply here, due to the limit on Wonder selection and the limit on Cities that can be owned. Such differences from a typical Cultural Victory would enhance the discussions and widen areas of Civ 4 that would otherwise have been explored in this scenario, making for a more EPIC SGOTM.
Further, rather than a possible relative repeat of the strategy used/discussed in some recent SGOTMs or WastinTime's 15 Million Points thread (Knights, Mercantilism, and tech beelining), I'd like to see your team have additional factors to debate as tradeoffs, including:
i. Maybe spamming a ton of Great Scientists won't be as optimal (think: Culture Bombs, settling Great People)
ii. Maybe conquering the world won't be as optimal
iii. Maybe a beelined tech path won't be as optimal (think: Religions)
iv. Maybe having the 1000-years-Culture-doubling effect be relevant will make for even more interesting Wonder-selection tradeoffs, as well as the timing of when to invest resources into completing them (think: less Failure Gold)
v. Maybe the relevance of a Wonder's base Culture will also make for an interesting tradeoff discussion
vi. Maybe dealing with the Apostolic Palace won't be as straight-forward (since an AI could still defeat you with it, especially if you are tempted to obtain said Religion)
vii. Maybe the timing of when to complete research on Scientific Method will make for an interesting discussion
Basically, I think that an approach of everyone targeting a Cultural Victory will actually greatly enrichen the scenario, due in particular to some of the unique limitations that this scenario imposes tying in quite well with a Cultural Victory.
I also think that teams which follow the spirit of the scenario (focusing on key Buildings/Wonders) will have a much more reasonable chance of competing against a team that will likely otherwise Lightbulb their way to the end game and treat the completion of most of the Buildings/Wonders as an afterthought, probably winning by a wide margin, but while not truly even playing the same scenario as are those who spend most of their time focusing on completing the Buildings/Wonders.
Essentially, treat it as a challenge to have to do a lot more out-of-the-box thinking, a way to enhance the scenario, and a way to allow for a lot more alternative approaches to the typically-winning, straight tech-beeline approach to shine.