Anyone who jumps your case over this simply isn't paying attention or is new to the game and hasn't experienced "the whole truth". Tesla has been making claims about Supercharger locations and opening dates since the beginning. They're not all wrong, but they're pretty far from all right. I'm pretty happy with the locations that are available and what's promised, but there's an average several months to several years delay in deployment. I didn't buy a Tesla until there were multiple Supercharger locations in the state - specifically enough to get me OUT of the state
But to answer the "raw math" issue, even if there are a couple dozen people trying to drive through Blytheville in a month, it doesn't warrant a quarter million dollar build of a Supercharger location when Tesla are operating with finite money and there are places where a couple dozen people are trying to drive through an underserved area in a single day.
That said! If you're going to a family member's house in Arkansas theoretically you should be able to plug in there, right? Even at 120v 15A (closer to 1.5kW) you'd be able to put around 80 miles of range back in the car in a day. There's also all the crazy options for combining two different legs of 15A, or using a 30A or 50A drier outlet, or whatever, to get a quicker charge.
Also, if you're coming in from the east on I-40 you might be able to juice up at Jackson and skip Memphis altogether. It's a little further gap, but if you're charging at your destination it could end up saving you quite a bit of driving.