While it is true that most LD condensers are optimized for cardioid mode, some assumptions in the first post are not quite correct.
Let's take double sided/dual membrane K67(or k47, c12) capsule as example. Now imagine only one side is active, the other is not and for all intents and purposes doesn't exist in cardioid mode. You get frequency response like this:
We are interested in the green line which is 180 degree response. Most people think of cardioids as if they reject everything coming from the rear. This couldn't be further from the truth. 180 degree response is just 5 db bellow the 0 degree response at 5K where our ears are quite sensitive. This 180 degree response is created by the sound hitting the FRONT diaphragm coming through the mechanical delay network of the capsule's backplate, and not the REAR diaphragm which is in this mode disabled.
Even though the rear diaphragm is electrically inactive in cardioid mode, it is still acoustically active.
Now imagine we activate the rear diaphragm in such manner that we form figure of eight pattern. And we do get indeed, with an ideal capsule, F8 pattern with identical responses. The sound coming from each side of the capsule is now dominated by the sound coming from both physical diaphragms. We have achieved this by applying polarization voltage, and now both diaphragms are engaged. But what happened to that green 180 degree response we had in the previous image which was created by the sound coming through the rear diaphragm and the backplate and eventually hit the front diaphragm in opposite phase? Did it disappear? Well that's the thing people don't usually think about. It is still here, masked by the electrical signal created by the rear diaphragm. It is still just -5db at 5K, and it is mixed with the electrical signal. However it is PHASE SHIFTED by the distance between the diaphragms (approximately backplate thickness)!!! Of course this is true for the sound coming from both sides, there is no front or rear diaphragm per se, the capsule is symmetrical.
It's easier to understand what's really happening, if you don't think about polarization voltages but think in terms of sum and difference. Cardioid is the electrical signal of the front diaphragm, Omni is front + rear diaphragm (in phase), Fig 8 is the front - rear diaphragm (anti-phase).
A multi-pattern LD condenser in figure 8 often has an almost perfect pattern, at least with quality microphones with a precision made capsule and good front to back symmetry. That's because the figure 8 pattern is produced by cancellation. The output represents the difference ins sound pressure between both diaphragms, which makes it a
near perfect pressure gradient transducer. What differentiates it from a perfect pressure gradient transducer would measure the difference in sound pressure on both sides of the same diaphragm. Yes, there is a small distance between both diaphragms. Let's say it's 6 mm (it's often a bit less). That would translate to a time difference of 0,02 ms. Not much, is it?
The difficulty with fig 8 is frequency response, i.e. getting good treble response. That difficulty is basically the same for "natural" figure-8 capsules such as ribbons and multipattern mics in figure-8 mode. And as has been said, multipattern condensers are usually optimized for cardioid. Thats especially true for most classic capsules. But there are newer capsule designs such as the Neumann K89 (U 89, TLM 170) and K107 (TLM 107) which offer a more linear figure-8 frequency response better than most ribbons. Here's a video with the TLM 107 in figure-8 mode:
Omni: Yes, technically speaking, the omni setting on multipattern mics is less satisfying. Frequency response wouldn't be a problem - if the mic was optimized for omni, which it never is. Still, there are some who do a pretty good job. Again, its the not-so-popular newer capsule designs such as the K89 and K107. Technically, the capsule output represents the sound pressure to both sides, so it is a near perfect pressure transducer (and as such has almost no proximity effect). But the large diaphragm puts limits to the off-axis response, so the pattern narrows considerably in the top octave. Another aspect that's usually undesirable: The top octave becomes directional to front and back. The rear lobe has no practical use. A single diaphragm omni becomes directional only to the front, so becomes less sensitive to noises from the rear (e.g. caughs and sneezes from the audience).
Still, although multipatterns in omni mode are less than perfect, some engineers put them to excellent use. The late great Al Schmitt preferred using U67s in omni mode. And the results sounded fantastic!