With no CFA, there would be less aliasing (ideally none in the constructed example). With the CFA, there is more aliasing (depending on scene, lens, etc). The act of introducing a CFA has a causal effect on the degree of aliasing. I don't get why this should cause much debate.
In practice, it isn't true.
The AA filter is chosen, for each and every system, depending on the specific sampling rate. That rate is indeed changed because a CFA is used... but that is true for any mechanism added to encode color information. Removing the CFA is not a viable way to reduce aliasing and should not be thought of as if it were.
The CFA (or another mechanism with the same base problems) is required if recording color information is the goal, and one pays the penalties for that. The base sensor design has to be higher resolution to record color, and the AA filter must be matched, if all else is to remain the same.
The sampling system (sensor) and the pre-filter stays constant in both cases.
The sampling rate necessarily changes when a CFA is used to encode color information. It is not reasonable to use the same AA filter for different sampling rates.
The difference of whether a CFA exists is a matter of whether color information is to be recorded. The design is of course optimized for that. Including a CFA is not based on resolution requirements.
The only change is the introduction of a CFA. This CFA alters the effective sampling characteristics of the system, by making the acromatic sensor partially blind for certain parts of the spectrum at certain spatial locations. If there is significant high-frequency spatial-chromatic detail, you will get aliasing.Indeed, but...
But that is also true if the sampling rate is changed for other reasons. Regardless of the reason, the proper AA filter is required, and it is necessarily optimized for the specific sampling rate.
I believe that Floyd here summarize the question that the OP seems to be concerned about: does the Bayer arrangement affect lower frequencies (such as would be the expected output of a high-quality downscale)?
The answer is yes, it can. If the prefiltering is unaltered when a CFA is introduced, you have the possibility of aliasing.
If the system is poorly engineered it will provide poor data. Mismatched design is not a component problem, it's a design problem.
A much larger significance of this with and without a CFA is the fact that with it the color information is captured, and without it no color information is later available. How much aliasing is of no significance by comparison, assuming one wants a color image!
If you introduce the (theoretically necessary) prefilter cutoff, you will (for practically available filters) affect lower frequencies, and you will render the camera far worse than what is possible for full-resolution output.
You are ignoring the fact that the "far worse" camera produces far more useful information, granted at lower resolution.
The theoretical answer is not complete without some practical consideration. I will hazard a guess that you would have to have some quite unusual scene for color aliasing to be significant/disturbing if you downsample a Bayer CFA image by a factor of 2x2 or more. Exotic bird feathers are my best bet.
Downsampling will remove high frequency
components. How the components come to exist initially is not a factor in whether they are removed or not. Hence if half of those components are real detail and half are aliasing distortion, or some other mix such as 1/4 scene and 3/4 aliasing, makes no difference. They are all removed by down sampling
Likewise not all aliasing distortion is high frequency, and therefore it is not all removed. For example if the camera does not even have any AA filtering other than the limited resolution of the lens, there is no reason not to have low frequency aliasing distortion that will not be dramatically changed by down sampling.
Rather obviously the CFA itself is not the issue! The sensor resolution and how well the AA filter matches it are the operative issues. The CFA is just a detail (in essence, is recording color information required or not) that has a known penalty.