Blue
Ravenous Bugblatter Beast of Traal
Some interesting ideas here, but be prepared for some serious resistance. For myself, I much prefer to go the other way: 3D6+6, drop the lowest. So the least you can get is an 8.
Over half the rolls of that are 15 or higher. Only abut 1 in 20 doesn't have a positive modifier. 35% of them are 16 or higher.
That misses the original posters points about wanting flaws but also about liking variation from rolls in the first place if they are uniformly high. As well as not playing nice with 5e's bounded accuracy.
It would fit a high powered / big dang heroes type of game, but in that case maybe blowing out the ability score cap would be good so there's still some room for growth.