The less time teens have on their hand, when they are actively involved in school/school activities; church/church activity; family and friend activities; volunteering or part-time jobs --- definitely all or any of this could curtail the amount of hours a teen would have available to become 'overly' attached to any one type of music.
That's the ideal for me.
Seriously though, would 'you' personally let your pre-teen
or teenager (13-16/17) listen to this type music constantly?
I think you're assuming the worst about young people. My brother and his friends don't do any of those things and they've been known to listen to aggressive music. Having been that age not too long ago I can safely say that the kind of people you're talking about exist in the minority, not the majority and although that kind of music isn't classy or age appropriate perhaps, it's still music and art.
Also I don't think one can become too attached to music. Saying that just listening to a rap song will make them want to do what's in the song is massively underestimating their intelligence. Young people aren't mindless automatons, they have the capacity to think for themselves, believe it or not.
Plenty of people, both young and old, listen to metal where there are lyrics along a similar vein and yet the vast majority of them are not out killing people dressed as vikings. The same goes for rap music. You can't judge someone in that way by their choice of music genre.
Never going to have kids myself but hypothetically sure, as long as I didn't have to listen to it. You can only teach someone morals and hope they follow them. If they've been taught well then they'll be fine, whether or not they choose to listen to rap music or not.
Actually, if my hypothetical teenager ever listened to the s***e that passes for rap/hip-hop these days I'd have to sit them down and give them some NWA, Beastie Boys, Scroobius Pip et al and sort them out.