A constant directivity design is one where the on-axis and off-axis spectral balance is maintained. Most of the speakers, even high end ones leave this so important factor out and instead focus on aesthetics. Its easier to sell speaker that look good with average performance than speaker that perform very good with average looks. Good aesthetics and good sound dont go well and the fact that sound cannot be seen, aesthetics take precedence.
So what does spectral balance of on-axis and off-axis mean. The goal of reproducing music is to fool the ear brain system. We hear on-axis sound directly and off-axis sound after reflections. Both ARE important. The on-axis sound comes directly, followed by the reflected sound. They should have atleast 10ms of inter arrival time. If they occur withing this window then our ear-brain merges them together, if its outside the window then it adds to spaciousness which is what we need. People try to suppress reflections but that removes the sense of spaciousness and makes the room more like an anechoic chamber. Too much reflections takes the clarity away from the sound. The right amount of reflections can be had by having a speaker that has off-axis sound same BUT reduced in SPL as compared to on-axis sound. Only constant narrow directivity speaker can do it, irrespective of drivers or crossover used.
Now toe-in the speaker, as one moves from left to right the left speaker sound increases due to toe-in and the right speaker sound increases due to toe in AND the spectral balance is maintained while the listener does so. Such a speaker strongly maintains the central phantom image when the material is mono or provides strong imaging when material is panned. Toeing-in regular speaker ie TM based designs is a futile exercise.
Lets look at dipoles, its a way of achieving constant directivity, it has figure 8 radiation pattern, in the bandwidth that it is used in, it produces same sound both forward or reverse, when we move to left or right the sound spectral balance is same, only the SPL changes. This is the biggest factor of sound being improved with them. Ppl think its because of boxless design but thats not the case. A wide dipole baffle broadens the directivity which is why a wider baffle should not be used with a dipole, it just defeats the purpose. Linkwitz made the lx521 with slim baffles.
Lets look at sealed designs, a 12" waveguide mated to a 12" midbass (xover at 1Khz) is what makes a good constant directivity design. Look at Earl Geddes's speaker Abbey (now defunct). He has much more content at his website, worth a read. Econowaves are also very very good at a slightly compromised vertical performance.