If fetal haemoglobin is so good at binding oxygen, why aren't we adapted to keep it until adulthood?

Firstly, although fetal haemoglobin is better at binding oxygen, it is also worse at giving up oxygen to the tissues which need it. Secondly, if adults had haemoglobin with the same affinity for oxygen as fetuses, the oxygen would be too tightly bound to the haemoglobin in the mother's blood to transfer to the fetus!