Your concern about numbers doesn't match reality. The UN states that at the current rate without anything else being done the human population will plateau around mid-century then begin heading down. The current fertility rate globally is 2.45 children per woman in her lifetime and has been on the decrease since the 50s. The countries with the highest also are the ones with the highest infant mortality and least social welfare - lowering their birth rates without dealing with these would have severe consequences.
Using birth control to control resources basically punishes poorer countries for rich countries stealing their resources. The world has plenty of resources, many parts of Africa are extremely resource rich which is why first countries and now multinationals backed by countries swept down, take them all for themselves and avoid any form of tax or fair price for their goods (the amount of tax avoided by one company in Zambia is ten times more than all the aid they get from the company's country of origin. Haiti's entire economy was thrown into disarray because an American company - possibly backed by their government - wanted to sell them pigs and agricultural resources so made up lies and forced them to destroy what naturally grows there). Fighting against technological, distribution, and tax, and the general injustice in the world along with greener reusable initiatives will give a far better resource than birth control.
And none of these have anything to do with taking a test to prove one is a good parent. You already proved it would be biased by having a very Western ideology as the presumed basis of it.