I think it depends on the relative power of the audience and the effectiveness of cooperation within the promotion.
When the audience turning on you is a stronger threat than that of losing to a rival, kayfabe situations are likelier to develop. But vice versa. In a lot of modern arenas, such as business between banks or competition between democracies where war is nigh impossible, kayfabe is highly likely to be present. There's not much room for major victories over your nominal rivals so you stop trying and instead focus on looking good rather than actually moving forward.
When the audience turning on you is a stronger threat than that of losing to a rival, kayfabe situations are likelier to develop. But vice versa. In a lot of modern arenas, such as business between banks or competition between democracies where war is nigh impossible, kayfabe is highly likely to be present. There's not much room for major victories over your nominal rivals so you stop trying and instead focus on looking good rather than actually moving forward.