Yes, PoS can of course be forked from bitcoin.  PoS has some theoretical problems, but at least, it doesn't need to waste $400 million a year on "cryptographic security", because PoS is cryptographically secure with digital signatures, not with "good guys can spend more electricity than an attacker".

PoS has, as a cryptographic security system, far, far more security than PoW.  However, PoS WITH REWARDS (fees and coinbase) is problematic, because you run into the problem of "nothing at stake".  PoS without any reward, purely voluntarily, like the people running bitcoin nodes right now, would be perfectly safe, because nobody has any "stakes" in minting fake blocks, apart from the ones wanting to double spend, but the PoS system can be made such that the probability that they are allowed to mint the block in which they double-spend is extremely small after a few confirmations.

My idea is that a PoS system without rewards is perfectly safe.

The way PoW is centralized in bitcoin, it would be a good thing to go to PoS.  But it won't happen, because bitcoin is "frozen in" now.  Any PoS fork of bitcoin wouldn't be called bitcoin, and as the name "bitcoin" is all it has going for it, that would be the end of it.