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.
I don't want to be rude here but it appears to me that you have very little knowledge and understanding of how probabilistic distributed consensus through the blockchain works.
"Stake models are not required for coin weight to equal network control"
What are you trying to say here? Coin weight in a Proof of Stake type model only deterministically gives you control if you own more than 50% of the coins.
From an economic perspective yes, if you own a lot of something you might be able to assert more control over it. But please enlighten me where coin weight equals network control in a model
where those coins do not directly influence the creation of new blocks or somehow restrict transactions.
"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."
Yes a finite
resource is desirable for a blockchain type method of consensus. In the original whitepaper satoshi points out why using network addresses is not a great idea and that using processing power
as a finite resource makes sense. If you do not require this finite resource the entire mechanism boils down to who is the quickest at producing the most blocks and disseminating them (actually such a system would still be valid but for obvious reasons it makes little sense to want it).
"The current Bitcoin model is already an obvious failure while people walk around in a delusional state pretending it isn't"
No it isn't. I do not understand why you think that the network needs maximum distribution of mining/minting to be secure.
Block height on top of the one with your transaction is a measure of confidence. Unless the attacker disrupts the entire process of transactions as long as your transaction is sufficiently low down in the chain it becomes extremely impracticable to be removed. Double spending is an issue that will always exist if you have randomness with the block creation method. That is why you should wait for a few blocks if you want stronger confidence in a transaction. It becomes extremely improbable that low down blocks in the chain will change.
Neverheless with a blochchain there is no 100% guarantee that a block does not change. The probability just converges to 1 that it won't. (I'm intentionally discarding checkpointing here as for this consensus is reached through a majority using the same software)