Because (1) it's not risk free, (2) it is painful, (3) it is quite costly over the longer term (4) you wouldn't want a 'pro-family' government to have access to

Because (1) it's not risk free, (2) it is painful, (3) it is quite costly over the longer term (4) you wouldn't want a 'pro-family' government to have access to a mountain of unfertilized eggs.