Sorry, I should have more clearly and fully described the kind of "cooler" I have. I was speaking of an Igloo brand cooler that I have had for about 25 years. Maybe 45 or 50 qt capacity. No wheels or other frills. It has thick walls filled with insulation, not simple voids. When new, the sticker on it claimed it would keep food cold 5 days in 90* temperatures. I bought 2 of them for camping back in the days when I still did tents. No plug-in of any kind. Being well-insulated and with the help of the blue ice block, it has been adequate for getting frozen food home. The blue ice may actually be overkill. I figure it is extra insurance to keep the inside of the empty cooler cool in the hot car sitting in summer sun while I am in the grocery store.
My inclination is to keep things simple where possible. I have no experience with portable plug-in coolers.