I'd argue that that's too late. An EMT crew needs to request paramedics as soon as they realize that the patient needs a higher level of care. A perfect example is a patient in resp. distress secondary to acute pulmonary edema shouldn't need anything past a doorway assessment by an EMT crew to conclude that they need paramedics. The paramedics can be responding while the EMTs complete their initial assessment, treatment, packaging, and moving to the ambulance. Once in route, unless there's an excessive transport time, I see very little reason to request paramedics because a condition declines unless the paramedic base is between me and the hospital (however being at the hospital is generally not worth the paramedic response).
Edit: Something I realized that I should have added and something that Anthony touched on. One of the reason I will call paramedics if I have a reasonable belief that the patient might require paramedic intervention now or in the immediate future. If an EMT doesn't call when there is a reasonable belief that the patient will decline during transport because there isn't an appropriate paramedic intervention at this immediate time, then everyone would be complaining that the EMT should have called for paramedics. This ends up putting the EMT in a 'damned if you do, damned if you don't' situation because they can't divine the future.