A horn will be effective in any given frequency range depending only on the size of its mouth and the rate of its flare. Bass reproduction from a horn is NOT bassless by default. Usually this happens when the designer compromises to much, and foreshortens the horn in order to get the physical dimensions down. A horn system is a lot more efficient than any other type of enclosure. At the same SPL driver in horn design has smaller excursion than in other type of boxes or in open air, thus horn driver will operate linearly, producing less distortion.
Parabolic horns are so inefficient that they are really of no practical use.
Of these, the conical is the easiest one to calculate and stuff into a box, but it's also the least efficient. Conical contours are never employed for bass horns, because of the poor response and the impossibly long horns that result. The exponential is the most commonly used, and is easy to calculate. It is probably the best flare trade-off high efficiency vs. low distortion. This is why a very large number of commercially produced horns feature exponential contours.