Maybe because if he did, then Crayak gets to even the field. Their identities might have been found out quicker if it were a bigger group. Also, giving them the ability to morph was breaking a major rule already. If he gave them the box it would be breaking the rules even further.
Besides they were kids. Six random strangers appearing in the same place at the same time. Getting them to work together was a trial itself. I think if he did give them the box, the yeerks might've won.
In the beginning the kids were there to uphold the front, none of them foresaw it as something they'll be doing for more than a few months, a year at best cause the andalites were supposed to come. Also the auxiliaries didn't really work out, most of them died used as cannon fodder.
Sure they may have wanted to help but things happen, people have their own opinions and their own desires. David was a special case but it wasn't as if they could see into his heart. They had no special device that allowed to see if the person was a controller or even if the person was good.
The more people, the more trouble and the greater chance of being caught and infested.
I think even with the box, they would've just hid it away.