But to be sure, would need to do the maths lol need to find someone good with proba and algebra and market economy to put the equation together to see if some prectible behavior is supposed to emerge through some factor who is made to be kept constant in the equation, even if it's seemingly random and clumpsy.
I think one is reading too much in what isn't there.
Well the only way to be sure it isnt there is still to admit the possibility
it's a mark of open mind to consider all theory equally unless proven right or wrong. The opposite is mark of indoctrination and there are plenty of non religious form of indoctrination 
2) he then realized that he needed to solve a consensus problem, because of the finite propagation delays on the network: what if some participants received valid transaction A, and other participants received valid transaction B, and A and B are spending the same tokens ? How to come to a consensus ?
=> he needed a kind of decision game so that at any moment, only one decider was going to decide upon the consensus, that is, the full list of accepted past valid transactions. As he didn't want (at first) a central authority, he needed a LOTTERY BETWEEN PARTICIPANTS. However, in order to avoid a sybil attack, he proposed to do the lottery with Proof Of CPU work. --> a lottery every 10 minutes.
But it's where I want to get at is that in this particular context, the pow is totally over kill to solve this problem, and if the goal is only to reach consencus in the simplest / more efficient manner, it's not the good solution.
In the context, it's like the byzantine general all know the criteria for what is considered good attack time, and can just rely on this know when to attack.
The criteria to sélect good block and transaction are not that hard-core to require this giant pow lotery.