Namely as you asked why should you give more credit to a doctor, scientist or engineer than God when dealing with matters that relate to their area of expertise.
Then Jesus said to them, "Give back to Caesar what is Caesar's and to God what is God's." That sounds like a sensible approach. Give experts their due when they talk about their field of study.
God does not speak against science or medicine. People who interpret what God says do.
Actually, what we call medicine today is two different fields. More
when you count specialties, but two basics. Doctoring and medicating.
Doctoring includes physical work. Setting bones, surgery, etc.
May not be the right word, but close enough.
Medicating is drugging people. The bible does talk about that.
Pharmakia (the same root word as pharmacy) is translated as
witchcraft in the NT. This is what the Greeks practiced and
handed down as modern medicine.
Too many doctors are in the pockets of pharmakia today. They
give out useless or harmful drugs to people who don't need
them. This include poisoning them with radiation and vaccines.
God made natural cures, and even better, ways to avoid most
diseases, including cancer.