As someone coming from a similar kind of home (though less country-ish aside from some Kenny Chesney on my mom's side), I kinda share the same snob glasses as you. Growing up with primarily '80s and '90s music, whether it be the pop or rock of that time, it took me a few years into really getting into hip-hop. In fact, I remember the first rap music I ever liked came from (surprise surprise) Eminem.
I think my main issue with rap or at least the bad side of it comes from Drake more than Lil Wayne (Let's be honest. Who else on the site remembers Lil Wayne having a hit song since like 2016?). Aside from a few songs like "Take Care" or "Nice for What", most of the songs I hear from him just consist of one nonexistent beat being played under a rapper who sounds completely under interested in whatever he raps about. Not saying he's the worst but I think he's a determinant of the other artists he inspired later like Future or Desiigner or Lil Baby or literally most of the "Lil ___" artists that aren't Jon or Wayne. In fact, I'm straight up baffled about Desiigner's big hit song entitled "Panda" which....let's be honest, everyone, is not a very good song. The song is literally about Desiigner comparing his car to a panda. The "chorus" only consists of the word "panda". And it was somehow popular enough to make the Top 10 of 2016.
That's another trope of hip-hop I'm surprised you haven't mentioned yet. All the songs about whatever car they're driving like Bughattis, Corvettes, Porcheses, whatever fancy car they have. It's easily as annoying as hearing Jason Aldean sing about his truck, but at least he sounds more invested and interesting than any of the Drake-influenced rappers who barely sound like they care about their own songs.
There's also the subsection of rappers who get more fame for being scumbags like 6ix9ine and Kodak Black but I won't even begin to dignify those people as artists. I'd like to think that "TROLLZ" failing to chart was what killed off the careers of these people.
Of course, like other people have said above me, I do like a few rappers nowadays. Big Sean brings back the fun Ludacris side of hip-hop. Kendrick Lamar brings back an edge to hip-hop that we haven't really seen in forever. "DNA" is still one of the songs from my dated Top 50 Songs list that holds up. It's those kinds of artists that prevent me from writing off the genre, but it's definitely the dull ones that prevent me from embracing it as a whole. As someone with a moderate stance on hip-hop, I do recommend listening to those other artists people recommended above because they are more the best representation of the genre than any of the kinds I've listed above.
inb4 i get a condescending comment from someone who suggests i listen to rap even though i sorta do