You have started a rather interesting thread. I have not read it all yet. I will just give two short experiences of mine.
I am mainly working with Bayer cameras. As good ones as I can afford. Currently my main camera is a Pentax K-1. Digital photography is fantastic for color photography. I really like it.
EXPERIENCE 1
The first time i saw very well made Foveon images, I said WOW. That was some clarity that I cannot really see with Bayer images. Remember, this was some years ago, so both Bayer and Foveon had fewer pixels. The difference is not that big any more. Still there though.
But, and here comes the catch. Looking closer at the super clear Foveon images they often look a bit strange. Details, that are a bit fuzzy on Bayer, looks a bit distorted on Foveon. This is mainly aliasing. On Merrill it is also caused by noise reduction IMHO.
So ... I went from WOW ... to ... Hmmmm.
Of course, making a huge print, maybe the WOW dominates.
EXPERIENCE 2
Bayer only sample one color at every pixel, so the samplings are out of phase and you get color aliasing. That is the major draw back of Bayer. You can improve this with more pixels, but really not fix it 100%. Otherwise, Bayer are very good at color accuracy as the color filters can be chosen with care.
Foveon solves the color aliasing problem. That can be very nice. It makes it possible to omit the AA filter without serious problems. Which makes sharper and clearer images (see above though).
But ... there are several new color problems.
One is blotches. Those blotches are created due to poor separation of color channels after conversion. The gray is not sure if it is green or magenta. Are they common? Nope, but they have a tendency to pop up when they are not welcome. Can you avoid them? Sure, I assume so. But I do not know how.
Another one is color fidelity. This is now much better. Quattro is very good. But (IMHO) older versions of Foveon has problem here. And it varies what problems from camera to camera. SD1 has a huge problem with red, that tends to be orange. Some older cameras have huge problems with green, that tends to be miscolored when photographing flowers. And I have even seen images of white beaches that are cyan. Bayer images tends to be cold or warm when they have problems with color, e.g. in mixed lighting. Which actually mostly look OK. But, Foveon images has a tendency to go away somewhere else in the color space, magenta, cyan, green, ... Which is much more annoying. As I said, I am not sure this problem exists with Quattro.
A third one is the need for NLM noise reduction. Without it, Merrill and Quattro would be useless. In our (Kalpanika) converter, you can turn off NLM. And, you will not like the result. Not at all. What is then NLM? It is a non local mean "smoothing". It works like normal smoothing by averaging, but you use weighted non local information instead of local. This leads to a non soft "smoothed" image, but at also means that the resulting image might be fake. I would not use Merrill or Quattro in scientific or medical applications. Because, the result might be a lie. Sometimes you can see this lie, when e.g. two green leaves are yellow because a nearby wall is yellow. Is this serious? Nope, not at all for artistic photography. You will not be able to notice it. I have only seen it twice.