Earlier quoted context omitted.
From my (limited) understanding, the high cost of malpractice insurance that doctors must pay is what drives up the cost of healthcare, more so than their student debt.
This has been conclusive disproven by comparing what happened in different states that enacted tort reform for medical malpractice. The cost of insurance dropped a bit, but there has been no effect the cost of healthcare provisioning.
However, this study: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3536953/ demonstrated that tort reform resulted in a larger percentage of growth in the number of physicians which would indicate that tort reform does have an important effect on medical care provisioning simply because tort reform, according to that study, resulted in a larger number of practitioners, which would, necessarily increase access to care.
So while tort reform may not have reduced costs across all of insurance, it does have an effect on medical care supply and it could have an effect on costs on a specialty-by-specialty basis.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5701901/
"An important consideration when interpreting our results is that our analysis provides evidence that the Texas reform had little influence on levels of health insurance losses, in the aggregate, across a variety of patient groups and provider specialties... As a result, if tort reform’s effects on provider behavior differ by the provider’s specialty type or the type of patient, then different analyses presented in the literature, utilizing different but relatively homogenous samples of provider or insured types, may yield conflicting results regarding the influence of malpractice exposure on healthcare cost and health insurance markets. Further research may consider how specific provider specialties and patient groups are influenced by changes in medical malpractice liability exposure."