If we were to use an elephant mother host to grow the fetus, once the mammoth is born, it is possible the herd will immediately recognize the baby as an anomaly and abandon it. Thus, this child is born into a world of suffering, not just for the herd that rejects it, but for the individual who is raised alone with no family, possibly by humans only. What will we do when the next one is born? Just put the two individuals in a space together and hope for the best?
De-extincting such a creature carries additional costs we don't know how to quantify. Once that first, lonely, individual is sexually mature, will it even want to mate? Will it have the social skills to accept other future artificially-born mammoths as part of its herd? We have no way of "recreating" the social environment a mammoth would need to thrive in order to bring a self-sustaining herd of the species into balanced existence.