OK Tom, you asked for it… 
It comes down to the physics/mathematics of the thing.
In theory you could construct any old scale you want - pentatonic, heptatonic, 10-tone, etc. etc., and through history and around the world there have been some odd ones indeed. While such a scale might sound strange to our ears, it might not be overtly dissonant as long as one only uses it for solo melodic passages[1].
However when one sounds two tones together, the business of dissonance/consonance immediately comes to the fore. Two continuously-sounding[2] tones will only sound ‘consonant’, i.e. in tune, if their frequencies are in a perfect integer ratio. If they are not, they will sound dissonant to a degree that depends on how far from an integer ratio they are. For example, the tenor drone’s fundamental frequency must be twice that of the baritone in order for the two to be in tune, i.e. they must be in perfect 2:1 ratio.
The tones actually coming out of a drone, chanter, or regulator are not in fact detected by the ear as a simple, single tone - otherwise we would not be able to detect the differences in “tone color” between clarinet, oboe, trumpet and uilleann pipe, let alone Rowsome and Colgan.[3] Fourier proved (in the 18th century IIRC) that any such periodic wave can be broken down into a series of simpler (“sine”) waves in perfect integer ratio with the lowest or ‘fundamental’ frequency, and we nowadays refer to those in music as ‘harmonics’. One aspect of this which is sometimes overlooked or misunderstood is that there is no such thing as “out of tune harmonics” within a continuously sounding tone from a single instrument. That is, the sound wave from any woodwind note must be perfectly in tune with itself internally - e.g. when the chanter is sounding a note, that note is composed of a series of harmonics which are in perfect integer ratios with one another, this is dictated by nature, if you will.[4]
This is also true of drones. That means, that when your drones are sounding, they are in fact playing not only three ‘D’ notes at (say) 294, 147, and
73.5 Hz, but they are also playing many more harmonics as well - for instance the bass drone may be (and probably is) playing
73.5
147 (that is, 73.5 times 2, same as the baritone’s lowest harmonic…)
220.5 (aha, here’s the first ‘A’ harmonic in the mix…)
294 (D again…)
367.5 (F sharp, but considerably flat of the “ET” F#…)
441 (A again)
514.4 (between Cnat and B on the tuner, a “very flat C”)
588 (D again…)
661.5 (E)
730.5 (Fsharp as above)
808.5 (This is approximately a ‘flat Gsharp’ in ET)
882 (A again)
955.5 (between Bflat and B in the ET scale)
etc.
(Not all of the above harmonics are present in detectable intensities for a given bass drone).
This explains a number of things - for instance, why the tone color of a set can be so strongly affected by the bass drone, since its harmonics are located within the range of notes on the chanter (approximately 294 to 1176 Hz).
These harmonics do not all fall particularly close to the frequencies of an equal-tempered scale in D=294 (I chose D=294, or approx, A=441, for convenience).
For each note on the chanter, a similar set of harmonics is present, for instance if the chanter plays A=441, harmonics of 882, 1323, 1764, 2205, etc. are also present. The relative consonance/dissonance (i.e the “in-tune-ness”) of a particular note on the chanter, relative to the drones, is a function of how well the harmonics of the chanter coincide with those of the drones, and vice-versa. As anyone who has ever tuned drones is aware, two tones that are “close but not quite”, where harminic consonance is concerned, can sound worse than two tones that are nowhere near each other. Thus the notes of the ET scale, with their multitudes of near-misses, can sound a lot more dissonant than notes tuned to JI (‘Just Intonation’).
The switch to ET actually changed western music in enormous ways - a consonant JI major third is extremely “sweet” and consonant, but the ET third is dissonant by comparison. Thus Western music’s use of major thirds changed dramatically once ET became the rule of the day - thirds are nowadays considered more dissonant than fifths, but this was not always the case. The consonance of the major third is especially sensitive to mis-tuning - the range over which it sounds really sweet is very small. Since we all grew up listening to ET western music we are used to a major third that’s slightly dissonant, but when the chanter’s F# is perfect against the drones (rather flat of ET) the sound is dramatically different.
For most notes of the D major scale the difference between ET and JI is small, well within the margin of error of most players and ears; notably different are the sevenths (Cs) which in any case are bendy and troublesome enough on most chanters that JI vs. ET is not the primary worry for most of us.
Note, though, that there are certainly harmonics produced by the bass drone that fall within the “accidentals” - similarly, the fifth harmonic of E is G#, the fifth harmonic of F# is A#/Bflat, etc. and so the harmonic series produced by chanter and drones end up covering these tones as well. Thus it makes sense to tune the ‘semitones’ to the JI system also.
In terms of “modernity”, from a world music perspective our current equal temperament system might be looked at as a bit of an aberration. Since drones are common in many types music throughout the world, and since the biology of human hearing is universal, most scales around the world must be based on perfect intervals.[5]
As an aside, all this matter nought if you’re playing with a box, since unless a box is tuned “bone dry”, the differences we are talking about fall within the range between the box’s two or more sets of reeds, whose tuning is intentionally spread apart (for what reason, I have never been able to fathom 
but then again some people like double chanters too…).
Bill
p.s. - I believe this has effectively used my internet time for the week. See you another time, I hope this was useful to someone.
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[1] - there is the caveat that the human ear/brain seems to have a bit of a memory for tones, coupled with “heterodyne effects” which cause certain harmonics to be “manufactured” inside our own ears, if you will… the combination of which means that even in solo melodic music the ear will find certain scales sweeter than others, cultural bias aside. A subtle effect we can ignore for now…
[2] - for tones that are percussive, slightly different rules may apply.
[3] - there’s more to tone color than harmonic spectrum, but it’s a key part of tone color or “timbre”.
[4] - interestingly, this is not true of percussion instruments, whose sounds fall off rapidly with time. Also, while the harmonics within a single note must be in perfect tune. there is such a thing as an instrument whose “admittance peaks” are not in perfect alignment - in fact this is true of all real-world instruments; that is, their resonances or “preferred vibrating frequencies” are not perfectly aligned. Poorly aligned resonances (‘admittance peaks’) mean that the harmonics are imperfectly reinforced by the instrument, or actually interfered with, which results in such symptoms as stuffy or dull tone, slow response to fingering changes, reluctance to play the second octave, bad octave tuning, etc. etc. This is also another reason why an “in tune” instrument often seems easier to play than a poorly tuned one.
[5] - As early as Pythagoras this was beginning to be understood in terms of mathematics. A few places in the world use really strange scales to our ears, but in at least some cases the “weird” scales turn out to correspond rather perfectly to the harmonic series of their (non-wind) instruments - for instance in the case of the gamelan. There’s a really cool book on this (if you like this sort of thing) by William Sethares called Tuing, Timbre, Spectrum. Scale in which he proves that a 10-tone equal tempered scale (that is, a scale based on 10 equally spaced tones in an octave!) sounds quite normal if the percussive sounds are composed of harmonics which are similarly spaced (something not possible with anything other than percussion instruments, by the way).
Do we really know that “just intonation” was an actual, conscious consensus among pipe-makers and players over the past couple hundred years?