Hmm. As to the "no one uses recording distances like that any more", I would still say it, because in the 1930s through 1950s, apart from a few experiments, that usage was for mono pickup by a single, well-placed microphone in a well-balanced concert hall. What tapers typically do is different: making a kind of stereo by putting two or more mono setups at roughly equal distances from the sound source(s), aimed and/or spaced apart from each other to some extent to create difference information. As you indicate, the loudspeakers project direct sound farther into the space than would occur without amplification, improving the ratio of direct to reflected sound at least in some range(s) of frequencies. And to the extent that there's a roughly even match of direct and reflected sound energy, conventional stereo miking techniques still make some sense. But what the loudspeakers project at the recording position vs. what's going all around the room is all very frequency- and room- and loudspeaker-dependent.
Again, as I've said, to me it never makes sense to idealize any one recording technique, or to invest one's identity in using it, because there will always be situations in which it's not optimal. The methods and tools to which you refer are all based on the assumption of acoustic sound sources in well-balanced, reverberant spaces--not the output of loudspeaker arrays in rooms of indifferent sonics. So I wouldn't look too deeply into these formally derived, mainly classical-music-oriented methods, except maybe for general inspiration.
--As for small vs. large / single vs. double diaphragm microphones: Yes, this mainly comes up w/r/t omnis because that's where the behavioral differences are most marked, and where large and/or dual-diaphragm microphones are at the greatest disadvantage compared to good small, single-diaphragm types. With apologies to those who've heard this all before: The fundamental point about polar (directional) patterns of actual microphones--as opposed to their idealized response at 1 kHz--is that when a microphone has different polar response at different audio frequencies, logically and to the same extent, it must also have differing frequency response for sound arriving at different angles of incidence. Those two things are inseparably two sides of the same coin. Conversely if a microphone has the same frequency response at all angles of sound incidence, it must have the same polar response across the frequency spectrum. (Before proceeding further, it's worth thinking through why this must be so, if one hasn't done so previously.)
Next layer: Because of the disturbing effect on the sound field caused by any solid object with physical dimensions greater than half a wavelength at 20 kHz, constant polar response across the frequency range is physically impossible for any pressure transducer of practical size. Very small measurement microphones come close, but are way too noisy to use as studio microphones in the modern era. All real-world "omnidirectional" studio/recording microphones are thus compromises of various kinds, and engineers over the years have learned not only how to live with this, but in many cases to take positive advantage of it.
This in itself is nothing new. Large, single-diaphragm pressure transducers were the first and only professional condenser microphones on the market for the first decade or so of the existence of professional condenser microphones for recording and broadcasting. Condenser microphones in their modern form were invented and patented in 1916 as measuring devices for the telephone company. Improved versions from Western Electric and RCA were marketed for broadcasting, public address systems, recording and film sound starting in the 1920s. Eventually Neumann entered the field ca. 1927, but again, made nothing but large-diaphragm pressure transducers for years. The pickup pattern of these early models was narrower at 8 kHz than any shotgun microphone is today, while at 200 Hz it was essentially omnidirectional. A polar graph published by Telefunken in 1938 for a second-generation Neumann "bottle" microphone is attached. This pattern was called "normal" back then; terms such as omnidirectional, unidirectional and bidirectional came only later. Aiming this type of microphone was obviously critical, but it maintained good "focus" at quite some distance from the sound source, as compared to an actual omnidirectional microphone. Plus these microphones were fully diffuse-field equalized; their excess high-frequency pickup helped compensate for the high-frequency losses of AM broadcasting and 78 rpm phonograph records of the time. Again, this huge divergence in polar pattern across the frequency range is mainly a function of using such a large diaphragm in a pressure transducer. For mono pickup, such strange-looking (but reliable and regularly repeatable) polar response was actually quite useful to engineers who learned how to exploit it.
Since the narrowing of the pattern is wavelength-dependent, if you miniaturize the entire capsule, the narrowing moves up in frequency to a corresponding degree, leaving more of the midrange truly (or very nearly) omnidirectional. The state of the art since the early 1950s has allowed "quiet enough" omni capsules to have about a 20 mm diameter (the active diaphragm area being of course somewhat less) and to be "omni enough" across enough of the frequency range to support the modern recording idiom, in which it's a definite advantage for the pickup of high frequencies to be narrower than the lower part of the range. Most diffuse sound isn't picked up with as much brightness and detail as direct sound is--and that is what listeners have come to expect over the past ~75 years of such microphones being available. Within a few years, stereo recording became important first in broadcasting, then in recording; the old, large-diaphragm pressure microphones fell by the wayside almost entirely.
There are smaller omni mikes that don't have as much narrowing of the pattern, but they're considerably noisier, and their relatively greater brightness of off-axis sound pickup generally detracts from the listening experience, at least with conventional spaced-omni recording techniques.
As far as the synthetic "omni" setting of dual-diaphragm capsules is concerned, I suggest that you look at the detailed polar and frequency response graphs from the best manufacturers that offer them--Neumann being the obvious example. Pressure transducers have better low-frequency response and pick up far less solid-borne sound or wind noise; they pick up low frequencies the same way regardless of distance from the source (no proximity effect); their high-frequency polar response narrows gradually and favors the front rather than both the front and back (note the "propeller-shaped" pickup pattern of most dual-diaphragm multi-pattern mikes in their "omni" settings); their impulse response is cleaner by a considerable margin; and being closed behind the diaphragm, they can be placed in solid spheres to enhance the frontal response in the upper midrange "presence" frequencies.
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