Older horns often have dips and peaks on-axis, even though the power response is relatively flat. The problem is caused by varying directivity with frequency. The dispersion varies, broader and narrower, and the beam goes on and off axis as well. What you hear is, as usual, a combination of on-axis and the power response, so it gets complicated. EQing the on-axis ruler flat destroys the power response and usually just sounds bad. For some older horns though, you can knock down the worst on-axis peaks and they still do a good job.
Modern JBL horns in particular have much smoother directivity than previous generations; however, the power response is ragged. But, that can be EQd by the speaker designer in the crossover. Look at the crossover for something like the DD67000 and you will see numerous traps for that reason.
Most speakers I see reviewed here don't feature what I would call a horn, it's a waveguide, used only to control dispersion. Yes, a waveguide becomes a horn at some high frequency; but if the horn cutoff is at or above the crossover frequency, I call that a waveguide. Conversely, a horn usually maintains horn loading well below the crossover. An actual horn offers an advantage in IM performance, as it limits the driver diaphragm excursion by the acoustic loading.
Note: At one point, this was a sensible reply to a question about horns. Honest!