You don't need a secret fork. You just need the community to split over some sort of doctrinal issue, such as already happened with the ETH/ETC split.

Only with PoS, there's no way to judge which fork is the "right" one. In PoW, miners vote with their finite hashpower. There's no practical limit to how many hard forks a PoS system can sustain because they don't rely on anything that's actually scarce.