Main point (for me) is directivity. Efficiency is nice, but not really a big deal, really good amplifier power is CHEAP nowadays (lots of good class D amps around). But if you happen to be a SET afficiando, then efficiency is more of a requirement. Ideally you'd like directivity down to where the room modal pattern starts to dominate things (around 300Hz).
The crossover gag is just that it's just a single capacitor, won't do anything much more than keep DC out of the horn driver. Would sound horrible, in this case. Though a lot of cheap cone tweeter 2-ways in the 70s used a single cap for the crossover, and weren't horrible in response (though "flat" wouldn't exactly describe them).