IMO, the only time when females should be needed is when a women needs a 12 lead done, since her chest has to be exposed.
However, if someone is complaining of chest pain, time should not be wasted, time is muscle.
Delivering a baby with EMTs around might not be comfortable a pleasant experience. however I cannot see how having women do the delivery any better. in fact the only real thing that will calm the patient is knowing that the techs are well trained and experienced.