That’s not much of a basis for qualified comparison here. Which JBL’s are those, and how are they (or the Altec’s) representative of a whole segment of speakers?
Look, I believe we’ve been here before, but there’s nothing to support the narrative inkling towards modern pro drivers, or even a range of older dittos, being in particular marred by breakup modes. There’s tons of great pro drivers and horns out there with solid R&D behind them, and they don’t suddenly turn harsh when pushed - believe me. If they did they’d be out of business. Of course you could find cheaper "weaklings" among them with sub optimum horn profiles, flimsy material choice, less than stellar drivers and overall execution, and they would be the easy and even convenient target for field coil-, beryllium diaphragm-fitted and lovely hardwood housed speakers like your no doubt great Classic Audio Loudspeakers to make a case against them.
@phusis You make a really good case- most of my experience with the speakers I mentioned didn't include any investigation of what was actually causing the harshness. I assumed a breakup because I got to compare a beryllium diaphragm made for the old Altec horn against the stock aluminum unit; I have to assume that difference really was on account of the differences in the diaphragms.
The JBL to which I referred is the JRX115. Seems to me we had an expanded version of that speaker in the studio that used the same horn driver. A lower (not rock concert) levels it was pretty convincing in the mids and highs. It uses a Titanium diaphragm in the midrange.
My CARs use a JBL tractrix horn which seems to work really well. He has since replaced this horn with a machined maple horn; but as I understand it his maple horns correct an error that was in the TAD maple horns he used to use.