FWIW, I have also had liability-only coverage on my own car for a few years and I rent about 10x a year with Hertz.

I used Amex Premium for a while, partly because I was concerned about additional drivers. But someone on here prompted me to read the policies of the coverage on the free credit cards and these all cover additional drivers too so that doesn't seem to be a problem. (I was misinformed or assumed that they might only cover the cardholder, and my usual additional driver is not a named cardholder, or wasn't. She is now on one account.)

Anyway, as noted, this free "secondary" coverage is just as good as primary when there's no other coverage. What might you gain by having Amex Premium? One of the main ones is a higher dollar amount coverage for loss to the rental car. The $25 Amex Premium covers up to a $100k car with some exceptions for certain exotics and antiques I think. Most freebie coverage is only up to $50k car I think.

Note in some states you can get a lower tier of Amex Premium with $75k damage coverage at $20/rental. This is what I used to use. I live in PA and that was available here.

One of the biggest issues discussed several times is how these coverages work if you are using points for your rental. Generally it is a bit iffy if your entire rental is points, and that goes the same for Amex Premium. The wording of the MasterCard agreement seems to allow for coverage as long as you have partial paid rental (not entirely free). So I had a 9-day rental back in the summer where I used a free week and paid for 2 days. I felt okay doing that.

Coupons and CDPs including any $$-off PCs don't count as a free rental, those are just a discount. Some of the terms say the entire rental must be paid on the card, which makes it iffy to have even part of the rental as an award. But on a regular paid rental this is not a concern.