I think you are too gentle on conventional medicine. It's not just that it can seem cold and impersonal, it can be practiced this way, it can be damaging, doctors can ignore the actual outcomes and health goals of patients.
Two examples: my father was for many years in charge of the GPs in our region.One thing that he was constantly trying to get them to do was test patients that had been put of blood pressure drugs to see if they were effective. The reason for that is the first thing they did when a patient had high BP was prescribe, often without seriously looking at lifestyle changes. Then they just kept those patients on the drugs. But they actually only work for a small percentage of people - others should be taken off because of the potential for side effects, cost, and also just because it's not great to have people on unnecessary drugs.
There was huge apathy from GPs about this. That tells you something about their practice of medicine.
The other example is my uncle. On a lot of psychiatric drugs for many years, his psychiatrist was constantly tinkering. Was it necessary - no one ever really knew. 30 years later, kidney failure, his doctors at that time started going through all of these medications that he was still on to eliminate them. Many were a mystery, lots there to deal with side effects caused by other drugs. No effort ever made to reduce them as it became possible. Some they decided were almost certainly implicated in the fact they had struggled to control his diabetes, and his kidney failure likely a result of the year on these drugs too. The mental effects of stopping all but one - he felt a lot better, brain fog decreased.
His bi-polar diagnosis also came under some significant scrutiny in later years, he was diagnosed back in the 90s when everyone and his dog was being labeled bi-polar.
Now, age may well have mitigated his mental health problems which isn't uncommon, and at the time they were better than doing nothing. But the fact is there was zero effort from any of his doctors over 30 years - and he had several GPs over that period - to look carefully at medications that ultimately have destroyed his kidney function which is likely to kill him within the next few years.
People don't only become skeptical of conventional medicine because they are silly. Just look at what's going on with gender medicine or some of the COVID stuff - it's completely unscientific. (Or even a lot of things in maternity services, for that matter.)
Once people lose trust it's difficult to get it back because it's not an area where most people have enough expertise to know who is practicing well and who isn't.