In other words eventually the nearest galaxies will one day become the CMB as the universe continues to expand until they are on the edge, until even they fall outside the visible universe and no photons/light outside our own galaxy will be capable of reaching us and the CMB disappears.
But yes, in the distant future, it will not be possible to detect the CMB anymore (and it's entirely possible that alien civilisations that evolve at that time would probably never have a model of the Big Bang because there would be no remaining evidence of it).
I understood that the CMB is not photons from plasma but the first photons following recombination (when the universe cooled enough that electrons and protons formed first hydrogen atoms). In other words the universe was plasma just before the CMB.
I suppose though, that if space is still expanding but the universe is infinite, this might temper it out but it doesn't seem like enough - it would have to be an expansion precisely tuned to on average send radiation to 4 kelvin so we only see a cosmic microwave background, and don't wind up being bathed in an infinite amount of whatever frequency of radiation.
Infinity is funny like that.
It turns out #3 is wrong, so it’s still possible we live in an infinite universe.
(Imagine an infinite, unchanging universe filled with stars that magically popped into existence a billion years ago. You wouldn’t have a uniformly bright sky because even though every line of sight will theoretically terminate on a stellar surface, in most cases there hasn’t been enough time for light traveling along that line of sight — e.g. from a star 10 billion light years away — to reach your eyes.)
You are inferring infiniteness also translates somehow to cosmic density and luminosity. By definition of an infinite universe the vast majority will necessarily fall outside the observable universe and never be visible to us.
As to luminosity, even now when we look up and see dark patches in the sky, they are in fact are full of stars and galaxies. The most famous picture ever taken by the Hubble, the “Hubble Deep Field”, was taken by pointing towards a dark patch revealing 10s of thousand of galaxies. These 10s of thousands of stars and galaxies still appear as dark patches in our skies because they are not sufficiently luminous to appear in out sky as light without the aid of telescopes to collect their dim light.
You've just looped it back around: expanding space gives finite, shrinking, observable universes. Which is just exactly the Big Bang theory.
EDIT: Dark patches in the sky though don't work with infinite light sources - at the very least you have to explain why far away ones apparently switched on in a finite time in the past. But that's the issue too - we're deliberately ignoring evidence in this discussion which points away from that - i.e. the red shift which shows us galaxies are rushing away from us.
There is nothing about Big Bang theory that explains the current expansion of our Universe (i.e. dark energy). In fact the Big Bang theory predicted our Universe should have stopped expanding and began collapsing on itself due to gravity (i.e. the Big Crunch), and that’s exactly why whoever can explain why the Universe is continuing to expand has a Nobel Prize waiting.
Isn't that only true if the universe is infinitely old as well as infinitely large?
Particularly when you get into issues like entropy, which is the only real determinant of time even existing. A finite universe has a natural direction of entropy - whereas an infinite one does not, since there's an infinite amount of mass and energy and as such no possible lowest possible entropy state.
It's actually worse then that though: an infinite massed universe by definition would contain every possible configuration of that mass somewhere within it. So you and I talking right now like this, our past and future conversations would also all be somewhere else in the infinite universe happening simultaneously.
A universe with an infinite amount of mass and energy in infinite space doesn't really have any sensible notion of past, present or future - because all possible pasts, presents and future, exist at all times somewhere within it.
This is actually untrue for many reasons, but one is that there are different kinds of infinities. For instance, there are an infinite amount of real numbers between 0.0 and 1.0, and none of them are pi. Just because something is infinite, doesn't mean everything is possible within that infinity. Again, there are an infinite number of integers, but none of the are pi or 0.1 or 37.5
That was the statement, a universe with a 1kg blob of matter every billion light years would be infinite massed, but would not have all possible configurations.