Chewy.com ships prescription cat food in two days for free. It's free shipping if you spend more than $49 (easy with prescription food...) or sign up for auto-delivery (which also gets you 5% off). They also have excellent customer service, easy to use website, and great prices. Auto-delivery is stupid convenient too since my cats eat exactly the same amount each day so my usage is very constant.
I'm not affiliated, just a happy customer. I didn't even know about it until I got an AMEX offer for them a few years ago.
Amazon "free" shipping seems very costly to me amortized unless you impulse order a whole bunch of cheap stuff very often. Paying for upgraded shipping on an as-needed basis seems like a better value. Or simply reduce consumption...
You're also comparing apples to oranges.