I think in Swedish (my mother tongue), "doktor" is an academic title, while "læger" is the occupation. I don't think that the English language makes a difference, but we do, and I would also say læger 100 % of the time.
Why is doktor being required when "læge" is the common word in Danish for doctor. In 3 years in Denmark and 5 days in a Danish hospital I never heard a doctor referred to other than as "læge." It is true doktor is a dansk ord but it is not in common use.