I did a statistical analysis and you are correct. The issue seems to be that crude birth rates from around 500CE and earlier are overestimated significantly. The bad source seems to be Kaneda & Haub, "How Many People Have Ever Lived on Earth?", where they assume a flat crude birth rate of 80 for all BCE dates. The probability distribution is just a function of pop and CBR, so it results in significantly decreasing modern birth probabilities.