Why is the speed of light used as the metric for cosmological distances, if it isn't definitive?

When the universe is described as expanding, units of light speed are the ruler used to measure this expansion, so it would seem there is some underlaying metric, that is expanding in relation to light speed and is not the metric defined by light speed.

Consequently there are two distinct measures of space. If the expanding one is the foundational metric, wouldn't that make it the denominator in this relationship?

Yet if the speed of light is the numerator, wouldn't we be discussing a "tired light" theory?

The fact is this theory uses the speed of light as the denominator. So the expansion is in relation to the speed of light. That would make it increasing distance, in stable space.

Similar to classic doppler effect, where the train moving away doesn't stretch the train tracks, just increases the distance.

The logic continues to elude me.