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. This is how people invent religions, by seeing purpose when there wasn't any. In my idea, the whole concept was rather simple: Satoshi wanted a non-centralized token transmission system, and needed to solve a few technical, and a few economical problems. There were already several elements lying on the table and he put them together (which is the merit he really has).
1) He needed to get rid of the "central bank". The block chain concept, where instead of tokens to be materialized, TRANSACTIONS were the fundamental element, was a great insight. In as much as it is impossible to prove that transmitted digital tokens aren't double-spent, if everyone has a list of past transactions, that solves the double spending problem. So the idea was to get all participants to get the full list of all transactions at a point.
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.
3) he needed also to create coins, and he realized that creating coins was going to give seigniorage which was going to undermine the belief system in the money. So he (though he had) a brilliant insight:
"the CPU work spent in winning the lottery to determine consensus, is going to be rewarded with new coins ; that looks fair, because 1) a priori everyone gets the belief that they could have won the coins and 2) people doing something useful get rewarded".
That's more or less it. I don't think Satoshi's insight went beyond that, but that was already quite something.
The rest consisted in:
1) working out the details
2) thinking about the consequences of choices made when working out the details.
One of the things Satoshi was religious about, visibly, was the fact that there should only be a finite amount of coins in circulation. He must have been influenced by the Austrian school and gold bugs. In fact, if he could have put them into circulation right away, most probably he would have preferred that, but as he now needed to emit them by people finding consensus, he HAD A SERIOUS PROBLEM: how to reward people in the future when all coins are emitted ?
In order to obtain a finite amount of coins at the end of the universe, he needed to diminish rewards ---> simple solution of block reward halvings. In order to reward them in the long term, he needed transaction fees.
In order to limit the coin emission, he needed the lottery to take place only once every 10 minutes, and because he didn't want to rely on real time (in the end, he did!) he invented the scheme of increasing difficulty.
The logical consequence of this was that the economic cost of the PoW at the 10 minute reward was going to rise to be about equal to the market value of the emitted coins. This would lead to totally crazy amounts of PoW, the rise of specialized hardware, and the killing of the original idea of just "a lottery between participants to decide who was going to decide upon consensus next with Sybil mitigation".
Satoshi's idea of having most payments done with bitcoin led him to understand that the block chain as he designed it, would have to grow at 100 GB a day.
However, as is often the case with inventions, when one sees the consequences that were orthogonal to the original design ideas, the right way is to discard the invention because it fails in implementing what one had in mind ; but most often, one perseveres in modifying the initial design goals so that the invention in which one has a lot of emotional and intellectual investment, ends up suiting the goals. I think bitcoin has been created exactly that way: when Satoshi realized (partially) that his invention wasn't exactly what he set out to do, but not being able to think of anything better at the moment, he considered that it should go ahead and modified his initial ideas so that they suited the thing he invented.
This is why bitcoin is the clunky thing we see it is, and not the thing Satoshi set out to design, but failed to do so: a digital peer-to-peer trustless, decentralized money and payment system for all to use.
One can of course always think that this clunky thing is what he intended to make, but this is like explaining why God, in his perfection, allows man to make war and allows him to suffer unfairness. Simply because there wasn't any god, there wasn't any masterplan, but things just happened, and they weren't designed this way or another way.