Even in an emergency you're virtually never the critical chain in the response.

First responders are. Bystanders are. The staff at the hospital are.

There can be cases in which it's helpful to advocate for someone (unfortunately in countries with private-payor adversarial healthcare systems this does approach a necessity at times), or to comfort. But that's a role that's very rarely time-critical.

Source: trained and experienced at first aid, treating emergencies, witness to numerous accidents and injuries (and on the recieving end in a few myself). There's an immense pressure and often an assumed obligation to be aware and respond. In terms of actually positively affecting outcome ... the role is grossly overstated.

The one critical exception is when engaged in remote activities (hiking, mountaineering, sailing, etc.) where you might be a required part of an initial help-summoning chain. That's the exception for most people.

Keeping a calm head, ensuring that qualified help *i

Who said it was about providing medical assistance of any kind?

What services are you proposing receiving at a hospital?

Knowing that a loved one (in my case, a panicking, confused, and hurt niece who was in a bad accident with her younger sister) is in said hospital so you can come there and support them.

I was her emergency contact, and my presence there meant the world to both her and her sister.