I would think that basic first aid is something cops are trained in. That way if it's taking time for an EMT to arrive but they're close they could render aid. Now I would never want a cop in a medical emergency, but I imagine this is the reasoning.
I think you are right about the stated reasons, but I suspect the actual reason is so that cops get more overtime and the additional opportunities to harass targeted populations.
It's funny to see cops complain about how they're supposed to show up for non cop stuff, and then when you tell them: good news, we'll shift some funding to EMT/fire/education/homeless shelters so you don't have to deal with this stuff, suddenly they're against it.
We live in a small town with a volunteer fire department and skeleton crew EMS. If it is a serious issue, often the cops will be the fastest ones on scene, and just hand off to EMS when they get there.
I'm not sure if it's like this everywhere in the US, but in the rural part of Georgia I'm from when 911 is called it is required that the police (or deputy), an EMT, and firefighters/first responder all show up to be prepared for any type of emergency. Doesn't matter what's reported to the dispatcher, it's kind of an all hands on deck until someone's on the scene and the situation is assessed.
Not commenting on whether this is the best system, but just an observation that might help answer your question.
It sort of makes sense because in theory a cop could administer CPR and do basic first aid. But obviously in practice they go into every situation guns blazing, so this is how you get shit like this.