Horn speakers are really bright?

While I cannot comment on commercial / lower grade horns, as I have not heard any, my reference is the four horn systems that my friends and I have here on the island. They are in systems that were fine tuned for decades, by the most hard-core audiophiles who have tried everything in their life (cost no object), and settled with horns. Two are Altec A5-based (with crossovers modified to Valhalla and beyond), one is a big Edgar horn (with the Edgarhorn sub!), and one is my own design from ground up (Altec 515/288 drivers).
A common feature in these systems is there is not a hint of "horn coloration" in any of these sounds. If you were blind folded, you would not be able to tell from the tonality that you are listening to horns (zero honk / shout), although you could immediately tell by the shocking naturalness, lack of audiofile "plastic processed sound", lightning speed, full size, dense substance, and lack of even a hint of compression or listening fatigue at any level that these are unlike any speakers you heard. You can play these at +20dB SPL compared to other speaker technologies and have less listening fatigue than with others at that much lower SPLs.

They all give an experience that totally messes with you, and makes you feel that these are technologies from another planet compared to mainstream stereo gear.

Horn speakers are a life-long quest. Do not even think to have them if there are problems in your chain elsewhere, as they will show without mercy when the emperor is naked. And most audio gear is definitively unflattering when there's nowhere to hide.

If you are curious about horns, try to find someone in your area who has done it to perfection, and listen to it. You may not be lucky to have anyone near you though.... or you might have several. YMMV...

My experience with horns:

Sadly, I was not exposed to mid and low level horns in serious hifi setting. Although I'm not sad about it, neglecting and not playing around with mid-level stuff.

My experience goes for VOTT & few other other Altecs, all in seriously "spruced up" shapes by audiophiles with massive audio life experience and refined systems that driver those speakers. In addition, my own experience with Altec 515/288 and a University coaxial horn driver.

So, based on these experiences I can tell that nothing reveals the state of your electronics, and also the skill of the crossover and cabinet designer as well as horns do. Even minute changes show up very big time and give a potent reflection of what is going on. 

It is more than convenient to blame the horns for all shortcomings in a system, as most speakers tend to throw a benign blanket even over severe flaws.

How do I know this?

When you voice your system with highly evolved horns, then other speakers will be able to deliver their highest potential as well, or reveal their flaws, which, when corrected, will elevate them quite a bit.

Horns are the ultimate frontier. I do not recommend to play around with them unless the rest of the system is already optimized to a very high level. Also, you HAVE TO play around with them. The ain't plug 'n pray. You need to invest serious time to optimize them - or your system. Is it worth it? Yes. It's a paradigm shift.