In many poor, underprivileged environments, children are not encouraged to do these things with income. Furthermore, a lot of the socially encouraged spending patterns make it more likely for indoctrinated children to fall back into patterns of poverty even if they have the motivation and capability otherwise to get out.
I'm not sure if you've seen how kids interact much but peer pressure is extremely strong and if you're off reading books and playing with Legos at an early age there's little guarantee that it will persist into puberty and beyond. Plenty of friends I grew up with early on had a lot of these interests but most fell into a typical lower/lower-middle class trap of drugs and sex (with partying linking both together, of course). There were some middle-upper/upper class kids that participated a little, but there are different forces at work for those kids entirely that makes it quite easy for them to escape a bad cycle with merely competent parenting skills compared to a completely overworked, overwhelmed single parent or split parent household that defines a great deal of lower income household living situations.
It's a bit exhausting to have to pick up all the citations but I can certainly find a good reference or two for the first part if you know a couple phrases. Firstly, there's a couple papers on the phenomenon of "acting black" that shows how even gifted black kids are held back by themselves almost http://news.vanderbilt.edu/2008/03/acting-black-hinders-gift... or perhaps as a set of papers by a Harvard professor that grew up poor and black in a rough area http://www.washingtonpost.com/news/wonkblog/wp/2015/04/30/me... This other paper explores how drug use is correlated with peer drug use but can be mitigated by relationship strength with the mother, which can be rather darn hard if she's working 12-hour days http://sitemaker.umich.edu/356.darnell/peer_pressure_and_dru... If you add in anti-social behaviors, being poor translates quickly into anti-social behaviors as the sort of "unproductive behaviors" that is being banded about in the thread http://www.researchgate.net/publication/232460627_Poverty_Pa...
We're not here on HN trying to solve the world's problems or something in comment threads anyway, so being a bit qualitative and subjective is something that goes with the territory of a lot of social science. We could go really rigorous but measuring people and behavior is really, really hard to do well without making the results of papers so narrow they're irrelevant for making meaningful social commentary arguments.
I'm not sure if you've seen how kids interact much but peer pressure is extremely strong and if you're off reading books and playing with Legos at an early age there's little guarantee that it will persist into puberty and beyond. Plenty of friends I grew up with early on had a lot of these interests but most fell into a typical lower/lower-middle class trap of drugs and sex (with partying linking both together, of course). There were some middle-upper/upper class kids that participated a little, but there are different forces at work for those kids entirely that makes it quite easy for them to escape a bad cycle with merely competent parenting skills compared to a completely overworked, overwhelmed single parent or split parent household that defines a great deal of lower income household living situations.