It is obviously easier to tailor a flat high frequency response using a diaphragm smaller than 18 mm as the peak frequency is in the order of 1/2 wavelength. For SD this comes to the order of 15 kHz while for a LD it is closer to 10 kHz. Although the behaviour beyond 15 kHz may be rather a matter of a few fetishists, it is obvious that a rapid fall occurs above the peak. This explains why many (even rather cheap) SD microphones exhibit a reasonably flat response up to 20 kHz while even highly reputed types such as a U87 have a steep fall off above 15 kHz.
Fine, except that it's not true...
The problem isn't with the diameter of the mic at all when you measure the on-axis response; a plane or spherical wave arriving on-axis isn't affected by the diameter in the slightest. Where the diameter makes a difference is in the rate of fall-off of HF as you move off-axis, and this effect is same, whatever directional pattern you think you are using. If you think about it for a moment, it's obvious; the worst case is a signal arriving at 90 degrees to the diaphragm - if a whole wavelength is present across the diaphragm it will cancel itself out completely. This effect grows the further away from directly on-axis you get; no effect at first, and the whole shooting match at 90 degrees (but see later...).
The on-axis response of my C414s, as plotted by AKG is pretty much flat up to 20kHz. It may well be flat above that as well, but their measuring system stops at that point.
As for the extinction frequencies, you haven't quite got them correct, I'm afraid. The relationship is f=c/λ, where c is the speed of sound in air. I do this in metric because I can remember the speed of sound in m/s, but the answers are the same if you use imperial measurements: So, c=344m/s, which means that for a diameter of 25mm (1") you end up with 344/0.025 = 13.76kHz, and for a 12.5mm (1/2") diameter, obviously the figure doubles to 27.52kHz. But as I indicated, this only affects the off-axis response, and because the case and mountings of the microphone will provide diffusion at the sorts of frequencies concerned, the cutoff is never complete anyway, and the dip often occurs at a higher frequency than you think it might - a glance at the C414 graphs suggests that this occurs at around 16kHz.
The second is: I admit that this often high overrated with respect to the sound quality but the frequency characteristics of SD types in general look better than those of LD types. This leaves open the question why both so many manufacturers as users stick to the LD types ?
For one thing, they are a damn sight more sensitive. What this means is that you can capture a lot more low-level detail from them without having to attempt to extract it from the capsule noise. Typically, the self-noise figure for 1/2" mic capsules is is around the 15-17dB mark compared to an equivalent 1" self-noise of about 7dB at best. So, in a typical vocal situation the overall sound tends to be more 'intimate' (for want of a better descrption) than the sound from a similarly placed SD would be, and this is pretty noticeable in a direct comparison. As for the frequency response - well, for mics intended for vocal use, manufacturers often allow a 'presence' peak to remain at around 7-8kHz, which adds a general sense of 'air' to the sound - but quite frankly you can do that anyway with EQ if you want, because the effect is pretty much the same.
So, it's not just myth/hype about LD mics sounding better for vocal performances - they really do, but it's a by-product of the sensitivity, not the FR.