I've seen the inside of one at summer camp back in the early 80s. It was a huge ceramic tweeter inside the center of that cone. I also guess the amp was poorly biased class B to save on battery life. This way, if the mic was left on, only when sound went through was there any current draw. It had only 4 x D or C battery cells above the handle and they lasted too long for a higher current drawing amp with tight biasing. It was all discrete components. The sound wasn't scratchy like you describe, or, like what I see in protest movies where event organizers have a cheap small megaphone where it sounds like the batteries are about dead, but, still, it's frequency range began above around 200hz to the upper 5Khz. Oddly enough, the outdoor speakers atop the telephone polls on the camp's PA system, which looked like 5x-10x larger versions of a megaphone's speaker, actually sounded really good, though, there was a 500 watt plugin stationary amp driving all of them in parallel in the office with one of those tall silver CB style mikes on a stand.
As for today, I guess people just don't expect better, so, even if parts improved, the design hasn't.
My guess, if you want a good sounding one, get a top-tier, top size one from the 80s, if you can find one in mint condition. However, they are much heavier than the ones today.