Reduced Awards =! Reduced Premiums or Costs
Texas seems to have set caps so low that it has reduced premiums for doctors. But "making malpractice cheaper" isn't much of a policy goal.
Nationally,'tort reform' caps have had mixed results. "...better-designed studies show that damages caps reduce liability insurance premiums. The effects of damages caps on defensive medicine, physicians’ location decisions, and the cost of health care to consumers are less clear." [0]
[0] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2690332/