Hatzalah is not just about the response time. There is also the knowledge of all the local medical facilities, and what each one is good for. They also build relationships with the local medical facilities, and can help push things along in otherwise overcrowded emergency rooms. But the main benefit of hatzalah is not something tangible that can be expressed with response time stats or a list of services. It's that feeling of calm and trust that we have built in knowing if something goes wrong someone who truly cares will respond and let you know the best way to deal with the situation.
When my wife and I had to call hatzalah, aside from the calm and caring nature of their response, the sense of calm we had even before we called knowing that we *could* call. There is that confusion at first, am I overreacting? Should I call an ambulance? Should I just go to the ER? Maybe there is a 24 hour urgent care? Maybe no one needs to be called at all? With hatzalah, you don't have questions. You call, they respond and they will know if the kid can stay home, if they need to go to a hospital, etc. Even the best EMS response is going to be doing what is necessary to cover their behinds. If that means spending Shabbos in a hospital, so be it. Hatzalah knows what that means to you and won't send you there if it isn't necessary.
What that does for a community is not quantifiable, and it can be difficult to describe what an incredible resource it is. One way to think of it for me is: for medical questions, the Rebbe often advised people to consult a "rofeh yedid". Hatzalah is a 24/7 emergency rofeh yedid.
+100.
I was once helping a relative who was recovering from a surgery due to a very badly broken bone. On shabbos he was in immense pain, to the extent that he was screaming in agony, and it was clear that he needed stronger medication than what had ben provided when he was discharged from the hospital. Hatzalah was called, and somehow they arrived *with a doctor and an orthopedist*, put the guy on a morphine IV, and enabled him to continue recovering at home. Had we simply called 911, I'm sure they would've transported him to the hospital, with similar results but being stuck waiting in the ER screaming in agony until he could get those meds, and having to deal with the stresses of a hospital on shabbos.
Another story that comes to mind is something that happened to my little brother when I was growing up. Hatzalah and 911 EMS showed up, and the 911 EMS basically said that for liability purposes they always *have to* advise that the best course of action is to transport to the hospital. The three hatzalah members who attended discussed it, and advised (off the record, also for liability purposes) that the situation was totally non-urgent, and that if we drove to the pediatrician we'd be just fine and we'd be able to avoid a very long ER wait at the bottom of the triage list. That's exactly what happened.
Again, during COVID I know someone who had relatively severe symptoms, and had been in the hospital earlier, was discharged and then things got worse, and long story short, Hatzalah responded and spent an hour calling all their connections to get in touch with the doctor that had treated the person in the hospital, and successfully tracked down the doctor and got the person some solid advice over the phone. That's not something that 911's EMS would ever do for you.
Another story that I remembered as I'm writing this- I'm close with a family who had a kid who was diagnosed with a severe illness, and on shabbos a few days later, the kid had some complications and had to be transported to the hospital. The mother was going to accompany the kid, but was an emotional mess, having learned of a pretty rough diagnosis a few days earlier. Hatzalah was able to advise that their poskim have ruled that a second person can ride in the ambulance on shabbos if the mother can't handle the situation alone. Again, without hatzalah there, the situation would've been much more challenging as the mother likely would've gone alone, with no support.
As
@Yehuda57 said so eloquently, it's about having someone there who truly cares for you, and who is willing to do whatever it takes to get you the best help.
If you want to see how they care, look at how hatzalah members get to a call and get into the house quickly, versus how public ambulance drivers (in my city, at least) slowly get out of their ambulance and unload their equipment. I remember watching an ambulance pull up across the street from my office last year when COVID had mostly passed already, and I watched the paramedics spend *5 minutes* getting all their PPE on outside the ambulance and unloading their stuff, before going into the call. If the patient was in cardiac arrest, those 5 minutes may have well killed him (though our 911 response time is so bad that he may have been long dead in that case, unfortunately).