Why does relativity not affect the speed of light?

[PeterDonis]

when flat-looking representations of spacetime, such as Minkowski diagrams, admit to being non-Euclidean, aren't they effectively saying they aren't really flat?

No. "Flat" in the context of spacetime means "Minkowski". More generally, "flat" for any manifold with a well-defined Riemann tensor means the Riemann tensor vanishes. Minkowski spacetime satisfies that definition.

I believe the tangent vectors you refer to apply to curves occurring within the spatial 3-surface

Doesn't matter. Any curve that stays within a spacelike hypersurface will have tangent vectors that are everywhere spacelike.

The lightlike velocity vector (Vmax) diagramed above is a tangent of the spatial 3-surface externally.

No, it isn't. No lightlike vector can be tangent to any curve that lies entirely within a spacelike hypersurface. See above. The fact that your drawing represents it that way means your drawing is wrong.

As with flatness, you seem extraordinarily certain.

That's because I am. I'm talking about precise definitions (of flatness) and proven mathematical theorems (about the properties of tangent vectors that I stated above). If you're not familiar with the relevant math, I strongly suggest that you become so. A good, if advanced, reference is Hawking & Ellis.

Your model describes but does not explain a universal speed limit essential to physics.

For your definition of "explain", perhaps not. For my definition of "explain", saying that the "universal speed limit" is a geometric property of spacetime is just fine as an explanation.

The model I gave does.

No, it doesn't, because it's incorrect. See above. An incorrect model can't explain anything.

 

[Dale]

My impression is that both π and c are ratios of separations, thus ultimately dimensionless

No, this is clearly wrong. Obviously c is dimensionful, its value changes with different unit choices and in SI units it has dimensions of L/T. In contrast, the value of π does not depend on the units and it has no dimensions in any system of units.

If you wish to pursue this line of reasoning, please provide a professional scientific reference which agrees with your reasoning.

 

[PeterDonis]

Though not peer reviewed, I don't think he's attempting to mislead anyone with his 24-lecture course on Time,

I don't think he's attempting to mislead either, but the fact remains that in anything that is done for a lay audience, scientists can get away with things that they could not get away with in a peer-reviewed publication. For whatever reason, it seems that few if any scientists are capable of not doing so. My personal belief is that, without the pushback of peer review to call them on it when they go beyond what is established, scientists, being human, simply aren't capable of being careful enough about what they say.