@quirk @ZachWeinersmith As someone with a doctorate in physics, I can tell you your understanding is incorrect. For one thing, nothing prior to the last sentence has anything to do with curvature, so the last sentence doesn't follow. And we do observe light behaving in exactly the way you describe, curvature or no curvature.
@doctroid @ZachWeinersmith your argument from authority notwithstanding, general relativity does tell us that, from the perspective of light, it travels instantly. From our perspective, it does not. We understand this as time dilation. So how do you account for the fact that light does have an observable speed limit in our universe from all perspectives other than light? Or has this theory been superseded?