There are a lot of things that depend on the speed of light. Such as what the spectra that different atoms would emit if they were heated. Yet the spectra for distant stars (that is, the light that was emitted long, long ago) has recognizably the same patterns as what we see today, except for a Doppler shift that we understand as having to do with the expansion of the universe. If the speed of light changed during that time, what spectra would look like back then wouldn’t match up so well with what we see today. Furthermore, if it once changed, why should it be so stable today? If can be measured so precisely the speed is now defined; that it doesn’t vary to 15 decimal places can be ascertained today. To within that tolerance, it does not.
Just because something is stable and steady today it doesn't follow that it was always that way.
Think of striking a match. When you do so the chemical properties cause the light and heat to flare greatly, before settling down to a steady, relatively stable flame.
If your perspective was limited only to a tiny portion of the time when the flame was steady and stable, would you be correct in your assumption that it was always the way you have observed it?
There's a reason. Insha'Allah. Yours not to reason why.