i save and then redeem AMEX points for pay-with-points only when buying a business class "insider fare" on AA/AS/DL.
you need sufficient AMEX points and an AMEX Biz Plat in order to have it make sense to book these fares easily (online, self-service) at AMEXTravel.com.
without sufficient AMEX points and an AMEX Biz Plat, you are stuck having to call Platinum Travel (and pay $39/ea fee) to pay with cash for these "insider fares".
absent an "insider fare", i'd redeem via Chase Sapphire Reserve portal.