This seems to vary quite a bit across countries which suggests to me that something can be done about it - I cannot say what though.

Parents can be encouraged and informed, to an extent, but the problem is that if they do not enjoy reading, you cannot pass on something you do not have yourself.

Another problem in the UK is that I think policy makers think of reading as a life skill, and education in general as preparation for work, rather than as something to enjoy - at least for the hoi polloi (or "the gammon" to use a disturbingly common term), their own kids are different.

FYI “gammon” is not at all a synonym for “hoi polloi”.