Why was hereditary slavery permitted in Islam?

I understand the justification for enslaving captives of war, including women and children at the time, but why would a child born to two already enslaved parents also be considered a slave? If the parents are already in Dar al-Islam, integrated into society, then why should their innocent child inherit their status? That seems like it goes against the Quranic principle that “no soul bears the burden of another” (la taziru waziratun wizra ukhra)—especially when there’s no urgent need for it. Also, I haven’t seen any clear Quranic or hadith evidence that the Prophet ﷺ actually allowed this. If I’m wrong which I 100% might be could you please share any sources and clarify the reasoning behind