Was going to avoid this discussion, but since All Darc was asking... the implant is called an intrauterine device (IUD). It's basically just a piece of copper placed in the uterus, and can be effective for a decade or more.
These should be made free for anyone that wants it since the cost is so low along with low side effect risk (since it doesn't mess with hormones). It's instantly reversible too just by pulling it back out.
Reproduction is a human right. In the not distant future (100 years) we will have the opposite problem of insufficient reproduction and we will have to devise ways to incentivise people to have children.
At some point we will need to implement some sort of genetic engineering since we have mostly eliminated survival of the fittest from applying to our species. Lots of tough problems to solve in the future, with lots of angry people on both sides of the debate. Ultimately we will have genetic engineering though, and after enough time goes by people will just find it to be normal, just like going to a hospital to deliver a baby is considered normal these days.