Suppose that the Energy distribution for a certain amount of light (as seen by earth) was given by
/- 1 if f < f0
E(f) = >
\- 1/f^2 if f > f0
Then we would have light "at all frequencies" which could be said to be "an infiinite amount of light" but the total amount of energy would still be finite.
Most of these explanations don't seem to first figure out whether if you had a uniform distribution of stars (at discrete points) in an infinite (Euclidean) space, if the amount of radiated energy seen at an arbitrary point would diverge if you summed over all available frequencies. If it doesn't, it seems like lack of sensitivity is the main issue here, and the cosmological arguments are simply additional reasons for why it doesn't happen.
From what I take it, you were basically simply asking, "what if the 'infinite amount' at 'all frequencies' were reaching you in a non-uniform distribution of frequencies? - would the original arguments and premises still stand?"
This assumes a minimum energy from each photon. If you could red-shift indefinitely you could end up with ex: 1 + 1/2 + 1/4 + 1/8 +... which sums to 2.
I believe the minimum energy of a photon is directly bound by the age of the universe, so if the universe was twice as old you could have photons at 1/2 the energy. You do get more light sources as you increase distance, but the inverse square law balances that. So Sum (1/n) from 1 to N which really slowly grows to infinity. As in 10^100 = 230.84
Of course, if there were an infinite amount of light (visible or not) reaching Earth, you'd be dead.