Reaction to the balls has varied from the start and not surprisingly, some people were very suspicious going so far as to establish a Reddit community rife with conspiracy theories. That some in that community believe the balls leach BPA is hardly surprising.
It's not mentioned what will happen to the used balls. A massive ball pit is always a possibility, but most ball pits that I've seen use multicolored balls and not just black ones. Recycling options are somewhat limited as black HDPE isn't all that common. (Black is common in film form, but I suspect the melt index for these molded balls is far too high for film formation.) I think the most likely outcome will be a classified ad in Plastics News:
For sale: 96 million used black HDPE balls. 4" diameter. Available for immediate pickup in Los Angeles California. Cash only (We're still flirting with backruptcy!). Special consideration will be given to businesses in the St. Louis, Missouri area (we feel really bad about taking back the Ram -- we really do. NOT!)