The CAP theorem is fundamental. There will be no way to solve it. You all can spend the next 1000 years fooling yourself will all sorts of designs, but they will also end up either inconsistent or centralized or unable to scale. PERIOD. PERIOD.
I feel completely relaxed about leaving out partition tolerance in consensus design; it is trivially obvious that there can be no consensus between parties that never have contact with each other.
Well I agreed with Fuseleer that Partitions can be created (for example those who will never have contact with each other or other scenarios), but this doesn't change the problem that consensus still needs to be attained within each partition and a global consensus is still needed for those who wish to spend to another partition; and afaics (after all our discussion and analysis) consensus will always require PoW or PoS. My prior post illustrated that even DAG requires PoW (yet it forsakes blocks which I think makes it more quirky).