K_ilpo_p, thanks for the excellent discussion . . . let me see if I can better refine and clarify my thoughts on the matter.
Also omnidirectional source directivity is constant, and in power response terms the driver type has no inherent effect.
The parameter of total, summed power response as I see it is most useful in trying to correlate the perceived timberal balance vs. measured frequency response for NON-constant-directivity systems, and for establishing the optimum placement and room treatment for a given loudspeaker system. It's pretty much irrelevant for the issue of establishing the best directivity characteristics of the driver(s) themselves. Consider that (for a single driver) electronic equalisation is supremely effective in altering the summed power response, but completely ineffective at solving directivity issues.
Altec made their Mantaray horns, using basically two flares and an abrupt joint between them. First expansion created the vertical pattern, opening into a narrow arc-like slit - being in itself a (horizontally) wide radiator- and the second flare controlled the horizontal pattern. The JBL Bi-radial horns use the same principle. In very simple terms a waveguide could be interpreted as the outer flare of a constant directivity horn, if you so wish.
While not all modern constant-directivity compression-driver waveguides use an abrupt change in expansion rate, I like your description, and find it a useful analogy. So I'll attempt to use it to illustrate my basic point in the whole matter - which is that to substitute a pistonic driver (cone or dome) for the compression driver and throat . . . brings out fundamentally different principles of operation in the waveguide as far as the directivity is concerned. Also, the difference between these two approaches is pretty much unrelated to the traditional view of the difference between compression drivers and direct-radiating drivers - which you accurately state as being efficiency, and acoustic impedance.
I do not understand what you actually mean with saying, that "for true constant-directivity performance to be possible, the wave-front propegation has to be constant with frequency."
Fair enough . . . my use of the term "true" implies a value judgement which I did not intend.
Instead, I'll refer to a compression-driver constant-directivity waveguide system (like the big JBL butt-cheek we've been discussing) as being a "wideband constant-directivity" system. In addition to the traditional points stated above (acoustic impedance and efficiency), a compression driver strives to transform the pistonic movement of the diaphragm into a pressure wave - a wave that has a shape that is (ideally) frequency independent. Early-20th-century practice viewed these as plane waves, examples being devices such as slant-plate acoustic lenses, and the driver measurement apparatus, a "plane-wave tube". And although the plane-wave as a useful, precise mathematical model may be completely outdated (I'll again reference Dr. Geddes' work), it is my understanding that in a "wideband constant-directivity system" (my terminology), the ultimate goal is for the driver to illuminate the waveguide in a manner that is constant with frequency. The result is a device where the useable constant-directivity frequency range is limited solely by the practical size of the waveguide, the mechanical performance of the compression driver, and the compression driver/phase plug/throat meeting the goal of frequency-independent waveguide illumination.
This is in (at least conceptual) contrast to the practice of using a pistonic driver to illuminate a waveguide, because the driver/waveguide relationship isn't (and cannot be) frequency-independent. Rather, (please correct me if I'm wrong) the idea is that the waveguide should dominate the directivity at the bottom of the driver's passband, and as the frequency increases, the directivity is decreasingly defined by the waveguide, and increasingly defined by the driver . . . this occurs because a pistonic driver will ALWAYS have an increase in directivity with an increase in frequency. Thus, in order for the driver/waveguide system to have smooth, predictable directivity performance . . . it is obviously of paramount importance that the driver itself have smooth, predictable directivity performance - in exactly the same manner as it should in a non-waveguide direct-radiating system.
My general conclusion is that while a piston-driver/waveguide combination can maybe acheive "a good practical approximation of constant directivity" (your description), its ability to do this will ALWAYS be limited to a much narrower frequency range than is possible with a wideband, compression-driver constant-directivity waveguide. It's also only effective over a specific range of desired radiation angles, which thankfully correspond to reasonably useful ones for studio monitoring. In the end, the directivity characteristics of the driver itself is the tail that wags the dog, and ultimately determines the extent of effectiveness in the waveguide.
As a final note . . . you make reference to the importance of matching the directivity of the bass driver(s) to the waveguide-loaded device(s) (something I very much agree with), and the effects of the crossover slope on the transition-band directivity. I'd be interested on how you view the common (recommended?) practice of turning i.e. the Genelecs sidewise and simply rotating the waveguide, which I feel makes a mess of these issues in both theory and practice.