I started this reply yesterday and left the window open on this computer. Since then, DSatz has posted a nice concise answer just as I hoped he would. I'll post anyway even though I'm really just parroting his more knowlegable remarks with more words.
Why go to all of this trouble? Well, I like the mental gymnastics, even if I'm not really familiar with it all. Second, and a real driving factor is: I'm poor when it comes to gear. Looking back on my original question the "What are the flaws" bit should have been in the paragraph above.
Well, there is the theoretical mathematical world and the physical world of applied ideas. I hope I can help satisfy your mental gymnastics quest and I think the understanding is important, but the real world engineering challenges of doing this satisfactorily in the physical world are hard to overcome.
Mathematically, a cardioid is the sum of a coincident omni and a figure-8. The positive polarity lobe of the 8 sums with the omni, increasing it's sensitivity on one side, and the reverse polarity lobe of the 8 also sums with the omni, decreasing it's sensitivity in the opposite direction. Overall the sum of the omni and fig-8 patterns is what creates the cardioid response shape.
Mathematically you can use the same technique with two cardioids to cancel out the omni part leaving the fig8. To do so you'd take two cardioids and place them coincidentally, with a 180 degree angle between them, invert the polarity of one mic and sum the outputs equally. You would be doing the following:
sum the outputs of: cardioid facing left + reversed polarity cardioid facing right
{substitute the omni + fig8 equivalent and read that as}
sum the outputs of: omni + Fig8 facing left + reversed polarity (omni + Fig8 facing right)
The omni terms cancel out and the fig8's are add together (because one fig8 has reversed polarity but is facing the opposite direction as the other).
But in the real wold there are problems:
>The cardioid mics aren't perfectly cardioid over the whole spectrum especially off axis and to the rear of the pattern.
>The two mics cannot be arranged to be perfectly coincident. The bodies of the mics get in the way. Unlike lining up capsules vertically to get them coincident for X/Y recording, even a small misalignment between them screws up the phase cancellations that are needed to generate a fig8 pattern, especially the 'null' at 90 degrees off axis. You would really need to get them as close together and as perfectly aligned as the back to back cardioid capsules in switchable pattern mics that use this technique to derive various patterns.
In addition you use up two preamp channels before summing the outputs to create one virtual fig8. So to make a M/S pair you then would need 3 preamp channels and a summing network for the two side facing mics.
However, if your are a bit of an electronics DIY type. I know of at least one M/S microphone kit that uses cheap cardioid capsules on opposite sides of a project box to derive the S signal. The capsules are in-line with each other but are separated by the width of the box, so it would seem the distance between them isn't the most critical aspect. I have no idea how well it works though.
Here's a link to the PAiA M/S mic kit. The schematic can be
viewed here.