There's a lot more to birth control than just dropping off boxes of condoms or the pill. You need a culture and a religion that allows it. You need women to have the freedom to employ it. You need men to allow women to make those decisions. You need men who are willing to accept the reduced pleasure of sex (from a condom) in order to prevent disease and unplanned pregnancy. You need education so people understand the connection between their individual actions, and the broader trends and problems of the society in which they live. Etc.

Just look at the U.S., where birth control is cheap, plentiful, and legal...yet there is still incredible social pressures working against its availability--even basic stuff like sex education, family planning, and condoms.

Poor people don't have children because they are bored, but because they are poor and they need the labour to work the farm. Or because they know the infant mortality rates are awful and children under five die from easily treatable illness (eg diarrhea, treatment a few cents of oral rehydration salts and some clean water).

there is probably more behind that than boredom. Maybe they want many kids to support them when they get older.