I've always expected an Edu-Startup to crack this problem by pairing an existing hyper-addictive game to more traditional homework.

My parents used to make me do quick one page math worksheets. Each sheet which took about 60 seconds earned me 5 minutes of time with "Command and Conquer", and to this day I'm able to quickly do Math in my head that most people would need to put on paper. My abilities drastically drop off at past the Algebra level.

If kids today had to memorize 5 new phrases in French while they were stuck in an Overwatch lobby, or something equivalent to get than new skin in League of Legends I think it could be a very powerful learning tool and not require the hands on effort from the parents.

That's actually pretty brilliant. It wouldn't be a language learning game but it would augment more formal instruction by assisting in building vocabulary. You could probably build in 5-7 new words a week and show 3-5 old words a week as well. Then of course you can put billboards and graffiti in a game where appropriate in the language using words the game has taught (or will teach).

In the load screens/waiting rooms it could be pretty simple too, the game could show and say the word then give you a grid of like 9, 16, 25 words to choose from and make you pick the correct one. The first few times you'd probably struggle but if you were playing for an extended period in a session, or over a week, you'd get that reinforcement every round/match/zone and be able to quickly select the correct words.

Typing of the dead is a great example.