I am NOT a right-winger, I'm a left-wing democratic socialist, but sadly, one of the reasons why private companies have alternate contact methods, and public ones don't is that private companies know that if they don't provide good quality service they will fail, whereas with public services, the employees will always have a job and will be paid whether customers come or not.
One reason why I prefer using private health services to the public ones is that they do more for you. I remember, in 2018, I had to take my father to a public hospital and my mother sent me back to find out what was going on. There was a kid with a vomit bag, there were two kids treating it like a playground and a man who had a hand bandaged up that was bleeding. And the room was full. And, there was a TV blaring! I had to go outside.
I often get anxious about making phone calls thinking, "Is the person I speak to going to be friendly?" "Will they tell me what I need to know?" I am pleased that we have online options these days. I prefer, if I have to use the phone, that I know when a call is scheduled for and to prepare accordingly.