Most people who experience psychosis don't experience it as a perpetual
    state,

Agreed.

    and they aren't particularly more dangerous while experiencing or any more
    dangerous while not.

Hard disagree. I have been in a mental ward. I have been in close proximity to people who have been undergoing psychotic breaks. Never have I felt in more danger for my safety, even though, ostensibly, nurses and other trained medical professionals were right there to deal with the issue. Being in close proximity to someone undergoing psychosis is a terrifying thing, and it's no surprise that traditional societies, in the absence of other mechanisms, would choose to exile people undergoing psychosis. And if the people never returned from their exile, well, that's a hard thing, but the great spirit must have had a different purpose for them.