You can waive the car rental company's coverage, at least for domestic rentals, without paying American Express if you have personal auto insurance. I do not understand the obsession with avoiding use of the coverage for which you have already paid.
Because:
1) there usually is a deductible on your own auto policy even if it is comprehensive.
2) your own auto policy premium will go UP and stay at a high level for the next 3 to 5 years.
I honestly think No.2 is the main reason why many who have small rental car claims that are, say, just above the deductible of their auto policy, end up not file for anything. Remember, the CC would require you to send in the DECLARATION PAGE of your auto insurance before they process your claim - whether the CC is secondary or primary (when you dont have auto poliicy or only the liability policy).