Just me thinking out loud: If anyone wanted a cardioid response , couldn't they place any speaker behind their main and feed it out of phase, filtered programme? Fiddle with delays in bands of frequencies, the overall EQ curve etc .. A spare mid woofer in a cabinet.
Would be similar to what folks do in the PA world with their simulation software.
Less coloured sound but serious Localization & Integration issues?
Well the die-hard cardiotics are still dancing around their golden calf
You can't have it all .. no free lunch!