There are essentially two fundamental problems. The first is with Proof of Work. Proof of Work needs to destroy value in order to be valuable. Proof of work is perfect to kill seigniorage, but is a totally horrible way to have "cryptographic security", because there's no advantage for the "good guys". The "good guys" are those that can waste most, not those that "posses a secret key" (which is the usual form of cryptographic protection).
The race to waste most leads to economies of scale (ASICS...) and hence to a concentration of producers of proof of work.
This leads to two problems: centralization, and the fact that those producing proof of work are not necessarily stake holders in the system.
But there's another problem, which is the fact that blocks are rewarded in the first place in "big lumps". This makes that there is a fight to make blocks, and to deny others to make blocks. As such, "making blocks" becomes a huge lottery with big rewards, where pooling together always pays against playing solo. This is a second vector of centralization: pooling.
Finally, the fact that there ARE rewards to "secure" the chain means that strategies to obtain those rewards are more important than correctly securing the chain, and to correctly process transactions. If fees are due, then there will be strategies to extract as many fees from the users as the market can bear, and not the optimal point of resource utilisation.
The whole system of blocks, that are rewarded, and that this reward is an incentive for people to "secure" the chain as by-product, leads to a dynamics that is centralizing, and far from optimal for the users and stake holders.
1. You don't understand PoW's purpose in the Bitcoin system, at all
2. You don't understand the value conferred by cumulative hashes in the PoW scheme
3. As a result of points 1 & 2, you don't even understand the blockchain concept
So why should anyone be expected to read your overlong posts when you don't even understand some of the fundamental ideas behind Bitcoin?
Because they contain valuable logical arguments, that go against some religious dogma that doesn't stand up to logical analysis by "bitcoiners".
Of course I understand the "value of cumulative hashes in a PoW scheme". It is a cryptographic securing ("signing") of a specific chain over another one ; the only way to make a "false copy" is to spend more hashes on the false copy.
Note that most cryptographic systems introduce an asymmetry in the difficulty for the "good guy" and the "bad buy". If I provide a signature of an original document, the making of that signature doesn't cost me a lot of effort, but for the one trying to make a false document with my signature, he has to essentially brute force my public key, which is an infeasible amount of work. This is why a digital signature is an efficient way of securing a given document.
If I were to "sign my document" with PoW, then I would have to spend JUST AS MUCH effort on making the signature, than the attacker. In fact, the one with more hash power would win: perfect symmetry between the "good guy" and the "bad guy". This is the problem with PoW. The "security" comes from the fact that we assume that the good guys wasted most.
If I have two block chains, in order to decide which one is the right one, I have to find out which one has most PoW. That is then the "right" one. With digital signatures, this is totally different: I check the digital signature against the public key of the signer, and if it fits, I know that the signer is the owner of the right secret key OR that the attacker has spend an IMMENSE amount of work to brute-force the key pair. With a block chain, I only know that the "good" one has wasted more heat than the "bad one".
As compared to a proof of stake system for instance, PoW is pretty lousy cryptography.
But it is a great system to waste seigniorage, and to allow newcomers without any interaction with the originators of the system to obtain coins.
It is a horrible system to "secure" something. Just any outsider can totally overrule the system, if he spends, say, 50 billion on it. The day the Chinese government wants to fuck up bitcoin, it generates 20 different block chains, that will cost them 50 or 100 billion dollar, and that's it. In a PoS system, that is cryptographically impossible.
The current Core threat is BTW funny. If they would switch to another PoW system, then bitcoin's chain would become MIGHTILY INSECURE, because there's not yet much hardware available for the other PoW system. So for a while, the amount of PoW (the amount of wasted effort) on the PoW on the new chain would be ridiculously small as compared to what bitcoin was used to, and with relatively small capital, one would easily 51% attack such a meager chain protection.
However, if bitcoin switched to a PoS system, the security would be entirely guaranteed. There would be no way to FAKE a PoS fork, because they are done by digital signatures of stake holders, not by having somewhat more hash power.