At age 6, I was learning to write 3 sentences that correlated with each other. Nowadays, children are learning how to advance to the next level instead of doing something that doesn't involve a screen. I'm all for the idea of allowing children to have phones, just not touchscreen/smart phones. Because once you introduce the smart phone into the picture, they're gone. And now the only world they know is that of the virtual one. I remember when I was a young boy, I played in my yard or maybe my driveway outside, and you could look around the streets and you'd see the exact same thing. Now, if you look in those same places, there's no kids outside playing anymore. They're all absorbed into the virtual world.
Six year olds are almost always with some sort of authority figure, if it's a parent, grandparent, teachers, aunt, uncle, etc. because of this, there is no need for a six year old to have a phone for him- or herself. "What if the kid wants to call Mom when he or she is with Grandma" well, use Grandma's phone. "What if he or she wants to talk to a friend on the phone over the summer?" When I was six, I barely remembered my friends when I was at home, which sounds bad, but little kids have a one-track mind most of the time. Even then, use a parents' phone.
As children grow older, they grow apart from their parents. They start to be out of the house, alone with friends, going on dates, etc. when a child is at that point (probably close to teenage years) is when parents should start thinking about getting a phone, or later. It really does depend on the child's maturity and how well parents will trust their kid(s) without an authority figure around. If that's a six year old, I guess so be it, but six year olds shouldn't be left without some sort of authority figure directly near them for more than a few minutes, in my opinion. Not smothered, but watched over.