Board Thread:Manga/@comment-39898841-20190622181312/@comment-33077628-20200717035820

Historia should have gotten pregnant soon after they learned that only those from the "royal bloodline" can use the full power of the Founding Titan, even if that meant the baby could eventually, in a last case scenario, be eaten by Eren in an attempt to unlock the Founder's powers without falling to the will of the first King. As horrible as it is, they were facing extinction against the Titans, and the alternatives were costing thousands of lives. So, Historia would have to get pregnant anyway, if for nothing else than to secure a royal bloodline, at least in regular human fashion.

Since Historia didn't get pregnant, even if Zeke had agreed to donate his sperm or to impregnate some woman, I imagine Zeke could die before the baby was even born, or maybe old enough to be turned into a titan big enough to eat him. Also, they would want to transfer Zeke's Titan as soon as possible.

As soon as Zeke got to paradis, they could have hooked him up with some nice country girls, saying they were "backups", in case something happened to Historia or her baby. But Zeke would probably not want to father any children, exactly because they would have "royal blood", and would have the power to undo what he was going to do. In fact, as soon as Zeke had success in the sterilization plan, he should probably kill Historia and her baby, to ensure the end of the royal bloodline, to secure his plan.