Predominantly the photons impacting the retina are the very photons that left the surface of the star. Some may have gotten "tired" along the way, read up on interstellar extinction, however that kind of mostly ish blocks the blue end, or more properly scatters it away from the line of sight from us to the star, thus artificially reddenning the light, but some of the photons from the star will be the same ones with just a bit less energy, and not enough to change the "colour" as far as the eyeball is concerned. Now, if you are looking at 3C 273 through a telescope cosmological red shift will mean the photon has lost energy and become reddened compared to when born. The atmosphere does this to a more marked degree, especially as you get nearer the horizon (looking through not only more air but also continuously denser air than just looking straight up).
As for coated lenses in eyepieces, I'm never quite sure what they do, never read up on it, although I very much doubt that they are passive image intensifiers as no wiring exists from them to your optical nerves.
On the sideways hand, the light from 3C 273 is not a billion years old. It will be of some age and some people probably know how to calculate that, because the limit is the speed of light in vacuo, and space isn't empty so the photons are nearly at the speed of late, thus relatively time hasn't passed much at all for them as far as their own reference frame is concerned (time dilation).
Something like that anyway, give or take a yard, ish, valid except for where I've got it wrong.
Personally there's an aesthetic to the view of something through a bit of glass relative to a screen. Sometimes after examining an object I'll just stick in a low power eyepiece and enjoy the field of tight crisp points of stars revealed against a blacker looking sky (sky can go a bit not quite black at high powers). A screen can no more emulate this than a photograph of a silver or gold object glistening or looking at a torch bulb directly, they just don't have the logarithmic range of t'eyeball.