Leaving aside the wealth gap factor, which I do agree is important:
When I think back to using computers as a kid, both at school(starting in 1999) and at home I don't think it's all that black and white wrt just playing at home vs learning useful skills at school.
At some point in the early 00s my underfunded elementary school acquired a bunch of old windows 95 computers. We would have classes where we mostly did basic touch typing, MS Office etc. At home, my middle class parents had also managed to find me some old outdated clunker. And yes, most of my time at home was spent playing games, chatting with friends on msn, pirating mp3s etc.
But I'd say I learned orders of magnitude more from my frivolous activities than from whatever we did at school. At home I was learning things like: online research(into warcraft cheat codes or quest guides for Runescape etc); software troubleshooting(having to reinstall windows because I downloaded malware on limewire or otherwise borked my install somehow); fast typing(from chatting with friends about whatever 12 year olds like to discuss.
Probably 90% of my typing practice back then came at home, not at school, and there was no touch typing. I could type 100+ wpm on just 4 fingers by the time I was in middle school. Never actually learned to properly touch type until I had force myself into it 5 years ago due to RSI); English as a second language(from various forums, irc, etc, hard to avoid back then); And I believe one of my first forays into programming was trying to get a cracked game with a broken .bat installer off TPB to work. I had a friend who got into it via Morrowind modding.
Actually, come to think of it, most of computer class was also in reality spent sneakily playing flash games and/or messing around with the computer settings just to screw with the next student/teacher to use it.
Even generalising beyond computers, I think a remarkable portion of the skills and interests that end up defining us as people, can be traced back to stuff we did trying to avoid boredom as children.
To summarise though, I do think computers have a place in school. But especially at an elementary school level, I think play should be a significant portion of their use, because play is how kids explore the world and themselves.
