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The speed of light is just a constant for converting units of time into distances, even if the speed of light were to change we'd probably choose to just change the units of distance to forcibly keep it constant.

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The speed of light differs depending on the medium it's transiting already though. I've wondered in the past if in the primordial universe time or space were different than what we've observed "now." It seems like they could both compress or expand like other physical characteristics of reality.

There's two different meanings for the phrase 'the speed of light'. One is the conversion constant I mentioned (which is currently used to define the metre in terms of time and is therefore constant by definition).

The other is the speed at which light travels (through a medium).

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