No, that's actually a thing, private or public. We treat at the scene, unless there is a need to get to the ER for something that we can't do. CPR, as an example, is pretty much the exact same thing when a paramedic is conducting it at a scene and in the ER. You might have some more people around, but the drugs being given and the device used to deliver shocks are exactly the same.* We have 'standing orders' for termination of cpr depending on how things are going (20 minutes and 30 minutes, respectively, for our agency), and we wouldn't be transporting the body afterwards.

This is also how it is in cases of obvious, unattended death. The cops get called, they call us, we throw electrodes on and print a flatline for the cops, and leave (the cops then wait for the coroner/medical examiner [medical examiners are fancier and only the big cities have them] who then leaves and the cops call [well, they should have already called] the mortuary/funeral home and then they take the body).

The point is, the hospitals don't want a dead body to deal with, so unless the person is alive or close enough to alive (I've transported 'corpses' that are having blood pumped by machines for organ harvesting purposes, it's really weird/unsettling the first few times) that they're still kicking, the ambulances don't transport. Looking at it from another point of view, we have live patients waiting on us to come, why would we waste our time transporting a dead one to a funeral home?

*not even kidding; the monitors on the back of the stretcher are often THE EXACT SAME as the ones hanging in the trauma room of the ER.