A fair solution is saying if you are on welfare, you have to get an IUD or injectable contraceptive as long as you are on social programs of any type. When you can support yourself and your children, or have a spouse who does, then you can have the birth control removed.
This allows those who can afford children to have them if they choose, because they are affecting others financially with their choice.
Those who cannot afford children then can't have them until independent, but it isn't irreversible like sterilization.
And you end the problem of people on welfare having more children, then being unable to go to work due to the high cost of childcare or stuck in poverty because of the cost of children.