I don’t believe that access to birth control will decrease birth rates or childhood illnesses.
If that were so, then there wouldn’t be an explosion of births among single women. Birth control is cheap and available everywhere.
This was a specific study of 9,000 women who had access to free birth control and often chose the long lasting options like IUD. In that population there were around 80% fewer teen pregnancies and abortions compared with the national averages. Perhaps if the rest of the population availed themselves of free long term birth control we would have a significant reduction in teen pregnancies and abortions. Long term birth control requires a doctors services and costs to put in place, so is not necessarily cheap or available everywhere.