By skyforbes First – eggs (and sperm) are not stem cells.
Yes, we can engineer stem cells from gametes, but we can engineer them from any living cell. Carol (and Diabete) leave plenty of those around. Making stem cells from skin or blood is routine science.
Second – eggs and sperm are actually the worst starting point if you want stem cells that match the person they came from.
They only contain half the genome, and it’s reshuffled by recombination. Every egg is a slightly different genetic lottery ticket, not the same genome Carol actually has in her body.
Third – the show specifically says the aliens need to harvest bone marrow stem cells.
That is significant and makes a lot of sense.
Bone-marrow hematopoietic stem cells are unique. They continuously make her immune cells that contain her exact genome, not a recombined variant. But more importantly they carry epigenetic marks, chemical instructions shaped by her unique history of stresses and illnesses. Those epigenetic marks are what make her immune system behave the way it does today. It’s why we harvest a patient’s own marrow stem cells before treating leukemia, to preserve their immune identity and memory.
And that’s exactly what the aliens need.
Carol is immune to their virus. To overcome her defense, they must tailor the virus to her living immune system. That immune system is encoded only in the bone-marrow stem cells currently inside her. Frozen eggs would give them a totally different biological starting point, basically a blueprint for a new, alternate Carol, not the one standing in front of them who has immunity.
The science on the show has been fairly solid so far, and needing bone marrow stem cells makes absolute biological sense for what the hive mind is trying to accomplish.