Intuitively obvious, attractively packaged misinformation, once it gets lodged in people's minds, tends to stay there a long time. People go out of their way to avoid evidence that would contradict or disprove such information--and when that can't be done, their response is often resentment, which reinforces the misinformation. Thus most attempts to correct misinformation not only fail, but actually backfire. No matter which side you're on regarding (say) Hillary's emails, Hunter Biden's laptop, or vaccination and mask-wearing for Covid, you will surely have seen this avoidance/resistance on the other side--but probably a lot less so on your own side, no? That's how it works with us humans.
Despite that, I want to explain what shotgun microphones do and don't do. The few who read this will have to decide for themselves whether to trouble themselves to change their thinking or not. I've changed my mind about some pretty basic things in my life, and I know that it can be a lot of trouble. Most people, being human, don't take on that trouble eagerly. Still ...
OK. We all know about directional patterns such as omnidirectional, cardioid, and bidirectional ("figure-8"). Many of us are aware that these exist on a continuum--the spectrum of "first-order" directional patterns. The three patterns that I just mentioned happen to be the two ends of the spectrum (omnidirectional, figure-8) and the center (cardioid). Anything else along that line is also possible--and that's where supercardioid, hypercardioid, "wide cardioid", etc. come from. There have even been microphones with continuously variable, remote-controlled patterns; the basic patent for how to do that is dated 1949, so it's nothing new.
If you have such a microphone, as you gradually vary its pattern from omnidirectional to cardioid (the halfway point), its pickup pattern narrows, and the microphone excludes room sound more and more, relative to on-axis sound. This narrowing and exclusion actually continues somewhat past the halfway point: The supercardioid setting (right around 5/8) is the one that excludes "all-around" (random incidence) sound the most, compared to on-axis pickup. But then if you continue, the effect reverses as the rear lobe gets larger and larger, eventually equaling the front lobe (= figure-8). By then the ratio between on-axis and random-incident pickup of sound is back to being the same as with a cardioid.
Note, please, that "shotgun" doesn't appear anywhere on that spectrum. That's because it's not a directional pattern, but a general way of constructing a microphone--putting a slotted "interference tube" in front of its diaphragm. The function of that tube is, as the name suggests, to arrange skirmishes between front-arriving and non-front-arriving sound waves, such that front-arriving sound is interfered with the least. But as a general rule, in any situation where sound waves are "played off against each other", at some frequencies and angles the interference will subtract (i.e. "destructive interference", the desired effect) while at other frequencies and angles it will add (so-called "constructive interference"). This causes the off-axis sound, depending on its angle of arrival, to be picked up with a frequency response that has very significant peaks and valleys. The longer the interference tube, the more severe the resulting response peaks and valleys will be, and the closer together (both in frequency and angle) they will occur. As you go upward in frequency, the peaks and valleys get closer together, to where eventually you have what's called a "comb filter" effect, which sounds like shit, to use the technical acoustical term.
That's one big reason why there are so many more short shotguns than long shotguns on the market, instead of people using long shotguns all the time. If you think that an interference tube adds "reach", then you would expect longer shotguns to be favored, no? Actually what the tube does is to cause a kind of semi-controlled chaos that has the NET, statistically AVERAGE effect of reducing certain frequencies off axis--but always at the cost of irregular overall off-axis response--and the longer the tube, the greater the irregularity at any given pickup angle (off axis) will be. I'm talking about 10+ dB peaks and dips within the space of one octave. Also, any relative motion between the sound source and the microphone can cause a significant change in sound quality because all of a sudden, the angles and thus the response curves will shift considerably.
As well, shotgun microphones each have a kind of "crossover frequency" built in to their physical design. Remember that sounds at different frequencies have drastically different wavelengths--there's a 1000:1 ratio among the frequencies we can hear, and thus a 1:1000 ratio among their wavelengths in air. If an interference tube is 1 foot long (i.e. somewhat longer than the majority of shotguns have), it will have no significant effect below the octave from 550 - 1100 Hz; the low-frequency and lower mid-frequency sound waves will simply flow around it the way that long waves on the surface of a pond flow around a rock. So any given length of interference tube implies a frequency below which the tube has no effect. The shorter the tube, the higher that frequency will be, and the longer, the lower.
Thus most shotgun microphones have no special directivity at low and midrange frequencies; they'd have to be absurdly long otherwise. Instead, because of who usually buys them, they're designed to reach full effect at the frequencies of the human voice that determine the clarity and intelligibility of speech, i.e. the region around 1.5 to 2.5 kHz. Above that range, the microphone's directional pattern goes all to hell--there's comb filtering like crazy. But with speaking voices it mostly doesn't matter, because the voice itself tends to roll off steeply above that range, and because the people who use shotgun microphones are very careful to keep the talent directly on axis at all times, while still getting as close in as they can without intruding into the frame of the video or film that's being made. And they never use shotgun microphones when they don't have to. Every professional film and video sound person has a supercardioid that they prefer for when they can use it for tight shots, sometimes hiding it in the scenery. Well-made supercardioids don't have the off-axis comb-filter response problem, so it's a lot less work to get good sound with them. (Radio mikes also come into play here.)
Finally, please note that such applications are predominantly mono. The problem takes on an added dimension (literally) when you try to use shotgun mikes in pairs to record music in stereo. Since they have one directional pattern at low and mid frequencies and another, varying and highly irregular range of patterns at upper-mid frequencies and above, there simply is no X/Y or near-coincident arrangement that can possibly be appropriate for their mutual placement. Any angle and distance that might be plausible for their low-frequency pattern is guaranteed to be wrong for their upper-mid and high-frequency patterns and vice versa.
On the other hand, shotgun microphones can be, and often are, used in professional film and video sound as the "M" microphone in an M/S pair. This can be done by attaching a figure-8 microphone to the shotgun such that their capsules are at the same distance from the sound source (the capsule of a shotgun mike is, of course, behind the tube and not at its tip). Some professional-quality, single-piece "stereo shotgun microphones" are also built on this principle. However, M/S recording only works when the mikes are close enough to receive a good balance of direct vs. reflected sound; it's pretty useless at the back of a room.
"When all you have is a hammer ..." -- shotgun microphones are very specific tools for a very specific set of applications. Just because you can hammer a nail with a microscope, you would be foolish to buy a microscope for that purpose.
Full disclosure: I do editorial consulting and historical research, on a free-lance and/or volunteer basis, for one of the world's leading manufacturers of very high-quality shotgun microphones, and the principal designer of those microphones has been my friend for many years. In other words, you might expect my bias to be in their favor--except that using them in pairs to make stereo recordings of music is a fundamentally misguided idea.
Which doesn't mean, of course, that you can never get a good, or even a wonderful-sounding recording that way. It just means that it's an unwise general approach where you're taking a bigger risk, and spending more for any given level of microphone quality, than you probably would with a more reality-based approach.
--best regards