After listening to several of the suggestions here and elsewhere, including Kayne West, Missy Elliot, Tyler the Creater, Snoop Dog, Tupac Shakur, Nicki Minaj, Flo Rida and others (I chose the best-selling names to see what's considered the cream-of-the-crop), I feel I have a better understanding of the reason for the chasm.
I think the rap that really irritates those of us who hate rap is the type that doesn't have any "musical" talent. They don't use "real" instruments, everything is created by moving a mouse around a desktop, the beats are monotonous and simplistic and the talking is monotone and not "musical." Those are artists like Kanye West, Jay-Z, Tupac Shakur, Tyler the Creater and Missy Elliot.
What I found after digging deeper is that there are actually "musical" rappers. I don't know what their whole catalog is like, but Flo Rida actually has musical songs, uses a lot of "real" instruments (or they're exceptionally well-sampled) and sometimes sings instead of talks. I even stumbled upon one Nicki Minaj song that was musical, but just one. So maybe like *pop, which I also dislike, there are a few decent songs.
Am I going to start "listening" to them? No. But I find them acceptable as background music.
* I watch Rick Beato's videos where he critiques the current pop charts. Recently he did the ten song-of-the-year Grammy nominees. All but a couple were pathetic three- or four-chord monotonous progressions with no time signature changes and no instrumental or vocal talent. And the couple that weren't were no better than background music. Most of the other chart-topping videos he does are universally unlistenable. I have to play some Dream Theater just to regain the brain cells I lost listening to them. Granted, pop has always generally sucked, but older pop at least had some songs that required talent.