This is exactly what's happened in Australia. Over-the-counter opioids (codeine, primarily) were banned last year. People were destroying their livers and stomachs due to overdosing on the adulterants (paracetomol/acetaminophen and ibuprofen) that were specifically put in to stop people taking them in bulk.

Now ordinary people with ordinary aches and pains can't get effective painkillers without visiting a doctor (or a quick trip to NZ where they're still available).