...POW ensures permissionless behaviour
PoW doesn't insure permissionless nor decentralized if mining is inherently centralizing.
There are many reasons that Satoshi's design is centralizing. One is for example that mining is profitable, thus there is a competition to drive difficulty higher and higher such that EACH transaction costs ~$10 in electricity (which is currently paid by "mining the investors" given that professional miners who have loans from the oligarchy+banksters mine with huge farms near hydropower at $50 per BTC cost and sell all that they mine thus extracting money from those investors fools who buy crypto as there is always a downward pressure on price). Even if no debasement was paid to miners, they have a monopoly on transactions added to blocks, so they can charge what ever transaction fees they want if they control 51% of the hashrate. It begs for a oligarchy on mining to develop (which is the direction it appears to be headed and normally government steps in with regulation to aid the oligarchy).
And increasing the transactions per block also forces centralization, thus furthering a trend towards oligarchy control, so saying cost per transaction will fall as transaction rate increases is only true if the resultant oligarchy decides to go for market share first (perhaps as a longer-term strategy of 666 enslavement and world government trend).
Also since mining is only done for profit, then pools are required to deal with huge variance of winning a block for typical (non oligarchy) miners. Pools centralize mining, even if we argue that miners can switch pools, the government can more easily target the pools even if miners switch since by definition there will never be as many pools as miners (not even close).
There are many flaws in Satoshi's design which make it entirely broken from my view. I can't support Bitcoin (nor Monero). I support things that I feel enthusiastically could work out well for mankind and be successful. Bitcoin will succeed only because it is fitting in well with the existing oligarchy's (e.g. Peter Thiel) plans for world domination (and that includes that an illusion of decentralization will persist long enough for the centralization to finally take hold).
It seems like you have hit an impasse, but without knowing the details of the problem
I had thought so, but I think I explained in this thread how to break the impasse I thought I had hit. But I reiterate I will go over all the details when I am offline to see if I haven't missed something in my thought process while I am writing here online.