Actually, I think it's me that's got it wrong, sorry. (fools rush in) But is the "resonance" the relevant thing or just the standing wave?
There are a number of wire antenna designs that use high order modes on a wire that's several wavelengths long, to increase directivity. The standing waves are there, whatever the length of the wire but the input matching can improve efficiency.
The 5/8 wavelength vertical monopole, beloved of radio amateurs, has significantly higher vertical gain than a simple 1/4 wavelength whip. It's the equivalent of a 5/4 wavelength dipole. I can see that there is a lot to be said for using standing waves in a dielectric dome / ring because it has circular symmetry. The metallic equivalent would presumably be a disc or dish reflector where there are images of the drive over the area of the reflector. I like the 2/3 size advantage for the dielectric system.
I think there must be a limit to the achievable aperture with such antennae due to losses over several wavelengths of path in the dielectric. I remember the problems with flat plate printed circuit slot arrays limited the useable aperture.