The simple solution is to simply make the customer to scan the item when they put it into the basket. It might be somewhat counterintuitive but in the end it makes better read rate.
The amazon thing is obviously based on computer vision which in the hindsight makes sense. And makes more sense than our ideas that includes CV as one of the source into sensor fusion magic...
And for the idea of doing RF magic for RFID: you to some extent want to do that, ant then you will find out that random Chinese sector antenna solves the same problem (obviously with the fact that it is simply not practical/possible to track everything with RFID tag that goes through the warehouse gate)
Yes, you'll have to recharge your shopping carts/baskets. Just design them to ensure they pass through charge (like a string of Christmas lights) when stacked together, so you only have to plug in (or have a cradle for) the bottom one (for baskets) or frontmost one (for carts.)
It's still a worse idea than using computer vision, if you've got that, but it's not something we couldn't have pulled off a decade or more ago.