The "benefit" so-to-speak is to just use the Amex Platinum card to get you National Executive status. Once you do that, you can pay with any card you wish when renting.
With regard to booking, you need to book at least a midsize car to be able to select a car from the Executive Aisle. It works pretty similarly to the way
Hertz Ultimate Choice works at major airports today.
In this case, whether renting from Hertz or National, there isn't a huge benefit to either company when using the card other than upgraded status, although as @
Yllanes pointed out, Hertz does give you an extra 4-hour grace period when booking via the Amex Platinum CDP. The same insurance benefits apply, and you still need to buy SLI at the counter to be adequately covered if you don't have a personal auto policy.