This is also 100% true of my dogs. As soon as there's a new dog toy in the house and one shows interest the other will begin to fight over it. There are some deeply-ingrained mammalian social behaviors that have nothing to do with technology, and won't change anytime soon. I'd be wary of blaming a phone ahead of instinct (though blaming businesses for exploiting those instincts is a bit different).
That said, I commend your efforts to try to maintain a happy medium for your family, that's really the best way to address these sorts of issues.