Your idea seems good at first, but I'm not sure it's the best idea long-term. For one, any movement caused by wind or by anyone moving around in the treehouse is going to cause the contact points from your brackets to rub against the bark. Over time, I could see this potentially damaging the tree more severely than bolts. Keep in mind that any part that's attached to the tree will also incidentally pull on parts of the tree that are attached to other parts of the treehouse. I would try to avoid attaching to any smaller limbs, and try to limit your attachment points to the trunk and perhaps a couple very large limbs that don't sway very much in the wind.
On the flipside, if your brackets don't damage the tree, they could restrict the tree's growth. If they don't damage the tree or restrict its growth, then as the limbs grow thicker in diameter they could move the treehouse's foundation and start to deform the treehouse, though this would take a very long time.
Family Handyman published a great article on building a treehouse, taking into account the tree's growth, using floating brackets, and many other practical considerations.