I currently work in the medical field and hope I can elaborate on a few things.
1) Doctors of all forms are under constant scrutiny and expected to operate within very specific guidelines in order to see patient and mitigate the risk of lawsuits from patients/families. Doctors are expected to use logic to proof or disprove problems and then develop a plan of care to solve it.
2) Most doctors are burnt out, over worked and actually under paid. Yes... they can cost a ton. Don't assume all doctors are rich and wipe their rear end with sheets of gold with diamonds stuck to it. I know plenty who don't make much more than I do and I am a grunt.
3) Most doctors treat SYMPTOMS and do not spend their time looking for solutions that might take years. This is how doctors learn and are trained now a-days. They treat the symptoms to make the patient happy. 95% of all appointments are cough, colds, bumps and bruises. Anything more than that means being sent to a specialist. The specialist then (under more pressure for being more than a normal doctor) follows even more rigid rules for helping the patient. They tend to pick the path of least resistance and the simplest answer because normally this is the case.
Adding the paranormal realm into the medical field is something no doctor would take on unless they had no other choice. The world is full of people who are skeptical of anything they don't understand, fear and hate things they don't understand, look for easy ways to use/abuse people to make money and given the constantly growing social/technical world we live in... no one wants to risk it. Law suits ruin business and take away medical degrees, bad word of mouth marketing ruins professional stature and drives business away. All things that make a doctor shy from anything that leaves them open to the bad things mentioned above.
To recap, doctors are at risk from all areas. They may believe in the paranormal, even be investigators, however the world we live in prohibits them from making certain choices in the care of their patients. Between Psychologists and other mental health providers there is always the chance to help decipher between an active imagination or the paranormal. It will take time and patience to make the proper determination about the abilities or problems of someone we love.