People who abuse birthright citizenships are, by definitions, not illegal immigrants. But even if you count all of them as 'unwanted' immigrants - how many % of total immigration to the US is result of those birthright laws?
Think two steps ahead, people aren't born right out of the sky. It encourages people to illegally enter for their citizenship baby and the parents remain illegal until ~21 years later when they can have the kid sponsor them. In the meantime the parents get free WIC even if they're illegal.
You are wrong about that. If an illegal crosses while pregnant, gets detained, and then gives birth the day after while in detention, that baby is 100% a US citizen.