To make it simple I quote the AvantGarde site:Did you read the paper I posted a link to? First page, 'purpose of a horn'...A horn can be used for directionality (think of the stadium speakers of yesterday) Key aspect here is loading of the driver, a much more efficient way of making air move leading to less distortion in the cone (just look at cone distortions at minimal excursion vs that at Xmax?)
Second page handles directionality
Executive Summary:
-Horns can be made to be directional
-Horns are efficient impedance transformers
-all cone speakers are increasingly directional with incrreasing frequency
-horn shape matters
I suspect you are confusing a design flaw for a characteristic.
" A horn funnel effectively guides the motion of sound waves and thus substantially increases the sensitivity and effectiveness of sound radiations. A horn is the most natural and powerful way to amplify sound. "
The consequence of this guidance is directionality . No directionality, no gain in efficiency.
Please remember that effectively the horn does not amplify anything. It simply matches acoustic impedances to maximize efficient acoustic energy transfer.
Or simply read it here: https://www.psaudio.com/askpaulvideo/are-horn-speakers-really-more-efficient/