PoS depends greatly on how random the minting process is (PoW has an element of randomness to it and this is crucial) or else you have a problem.
If I can split my stakes in a way that guarantees me to be chosen for block minting for x blocks in a row I can attempt attacks.
Stake models are not required for coin weight to equal network control. A finite variable is needed in the system for it to function, but it doesn't have to be coin age, coin weight, or any of the variables that have already been attempted. Models already exist like this, such as BitsharesX, that use other variables (reputation), although I consider their system completely broken for numerous reasons, a few listed below.
The current Bitcoin model is already an obvious failure while people walk around in a delusional state pretending it isn't. It's advertised as requiring "no trusted 3rd parties", yet the entire thing relies on them in the form of a small number of mining pools for block verification. Since Bitcoin never solved the "no trusted 3rd parties" dilemma, it's time to admit that and come up with a solution, most likely assign a performance metric to regulate those parties (i.e. PoS with reputation variable).
Unless every single iota of Bitcoin dev manpower is redirected towards the solitary goal of getting rid of mining pools, they're operating under the textbook definition of insanity.
Bitshares did it in an extremely poorly designed way by having an IPO where it's possible for the dev to to create thousands of mule accounts, send BTC in with all of them, get infinite premine + all his money back, then have plutocratic voting to determine delegates based on who owns the most coins afterwards. The entire thing is a train wreck. You can't get rid of mining for distribution, amongst numerous other changes they would have to do for how their system works to make it not a blatant scam.