Probably at least 90% since you need a prescription for most of them. But then you might wonder why its not 100% if you need a prescription. Well some people either sell their prescriptions to make money or their prescriptions are stolen to support the addict.
It's not so much the physicians fault. It's the structure of how the medical industry functions. Doctors rarely if ever combat what a patient requests. A patient complaining of pain is easily prescribed a pain killer by a doctor at the request of the patient. It's the patient who wants the abuse because they want the effect. This is only ONE case aspect. There are dozens of ways in which opioid abuse works.
Some people abuse it purely on wanting to be more hyped up for the kind of work they do. Many people in fast paced businesses with long working ours use them to remain stimulated so they can stay focused on their work.
Also big pharma wants to make a profit for it's share holders. The only way to do this is to push drugs out like they are candy. So they give doctors kickbacks for how many prescriptions they write. So doctors have an incentive to prescribe meds that people really don't need.
We don't have a preventative care system in the US. We have a reactionary one. Reactionary is the WORST type of medicine, because it rarely ever gets to the core problem and solves it. Instead we just treat the symptoms instead. Leaving the core in tact so that a patient becomes in chronic need of a drug. Which the industry wants. It wants life time buyers. If they produced a drug that cured you and you never needed it again, it wouldn't want to offer it.
Same for cancer research. Big pharma would rather have "treatment" medications that just help regulate your cancer. If there was a drug that completely removed the cancer they wouldn't want to sell it. Not unless a patient was willing to spend hundreds of thousands of dollars for the cure.