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.
I entirely agree. PoW is a total disaster. Thanks to a lot of discussions with @iamnotback I realized HOW MUCH it is a disaster.
The criteria to sélect good block and transaction are not that hard-core to require this giant pow lotery.
Indeed. Moreover, as I recently saw, Satoshi even foresaw that this mining would become totally centralized, defeating the purpose ! It is totally ridiculous to introduce PoW to avoid a sybil attack, and then come to the conclusion that only a few big players will decide on the consensus as a consequence of his "solution".
This is why I think that Satoshi, after he finished the outline of his invention, accepted to modify the design criteria he put forward himself, because his design didn't fit it, but now that he made it, he didn't want to discard it.
That is like wanting to make an airplane, finding out it will not fly, but it will float very well, and declare in the end that your were actually designing a boat !
In the same way, Satoshi wanted "money for everyone to use" and then put in a 1 MB block limit, making it impossible for this to be used as money for more than a few geeks on a few obscure trading places.
Of course, all this can be the work of an evil genius. But Occam's razor makes me believe that this is just a guy in his basement, doing the best he could, and the best he could, he realized, wasn't good enough for what he set out to do, but that wouldn't stop him. Don't put on the shoulders of conspiracy, what can be explained by ignorance.