Geddes posted some raw data regarding in room responses including dipoles. I suspect the emphasis on cardioid response misses the obvious aspect of OB designs - limited contribution from cabinet resonances.
After decades with panel designs (and the necessary positioning fussiness) I concur with Geddes conclusion and shifted to Constant directivity as my polestar to follow.
OB designs can be compared to ported cabinets, where considerable energy (at 180° polarity to the primary signal) is directed away from the listening position and arrives at the ear a significant time later.
This would be perceived as reverberation.
I leave it to our Gentle readers to determine if that is preferable.
http://www.gedlee.com/Papers/papers.aspx
I don't follow your first sentence.
One could make a cardioid basically on the same way as a dipole.
You just block the backwave with damping material or similar.
This is basically what the guys at Dutch & Dutch do.
It is also possible to make a carioid out of closed speaker (or BR for that matter), but the same counts for a dipole system.
There is no perfect, one way or another. They just have their advantages and disadvantages.
The constant directivity always counts, regardless whatever system you have.
The comparison vs ported cabinets doesn't make any sense.
The port and speaker work as one, ports can also be on the front etc.
Also the frequencies from a BR are way to low to cause any reverberation.
Unless you're talking about the internal resonance/standing wave and bleed through from the port.
But that is a different story, and either just one small band or side effect.
A good engineer/designer takes care of that.