Where were you checking? Where I look it cost a small fee. Maybe not so small to a poor person.
Beyond that, we're not talking about exorbitant fees for replacements. In Virginia, it costs $12 for a replacement birth certificate. In DC, it's $23. Not what I'd call major hardships. And even if they are hardships, a birth certificate is just one form of ID they can use. How many people, poor or not, have no form of photo ID?