Actually it is. Various physical constants are tied together. The spectrum of stars tells us of the chemicals in them. You could ask a chemist for more details. Change the speed of light and you would change all sorts of things. It would show up in the spectrum that chemicals absorb.
But for something easier to understand here is an article about a relatively close supernova. It was 168,000 light years away. Due to a rare set of circumstances they were able to measure its distance using triangulation:
A6. The Distance to Supernova SN1987A and the Speed of Light When supernova SN1987A exploded, its light soon struck a ring of gas some distance from the star and illuminated it. As viewed from Earth, the ring appeared around the supernova about a year after it exploded. Its angular size combined...
infidels.org
That light took 168,000 years to get here.
As to feathers, they provide warmth. Penguins have feathers. They cannot fly. They provide other benefits too. Ostriches would probably get very cold at night without feathers. But they also use them for display purposes for mating. Peacocks can still fly, but the importance of display for mating purposes is clearly stronger.
And then of course there are many dinosaurs that had feathers. Trust me, a lot of those bad boys could not fly.