Cost per mile of a battery change is different depending on driving style and how you charge your car but a short example might work out like this:

Let's pretend for the sake of arguments that we're talking about a Tesla Model S, and also let's pretend that you drive a lot and are completely unable to charge at home for whatever reason so you are forced to use high-speed superchargers as your only charging method. (this method of charging degrades the battery faster)

There are Tesla Model S cars now starting to stream back to Tesla for battery replacements. Most of them are owned by the same company that is doing testing of EVs and other technologies. One thing that is interesting is that these battery replacements are commonly reported as being $30k online, and most of these Tesla Model S vehicles that are needing these new batteries have about 400k miles on them

That puts the cost per mile for a replacement battery pack at 7.5 cents, and if you charge at home on a slower charger, the battery will last longer bringing this cost down. Factor in the cost of electricity and you're still winning by driving an EV, even if you ignore stuff on the ICE side like more frequent brake jobs, oil changes, and regular maintenance that happens on engines by the time you hit 400k miles (timing belts, spark plugs, etc)

Plus 400k miles is a lot of miles, most people don't get that far, and if they do it's going to be many years for even the average high milage driver. By that point in time a lot more EVs will be on the road and the economies of scale will kick in and batteries will be cheaper.