Bitcoin, the way Satoshi Nakamoto designed it originally, was not supposed to face such a situation in which nodes and miners are almost two different, sometimes conflicting, groups of actors.
I don't think so.
It is obvious that you can never prevent people from sharing a "computational work", and that's exactly what pools are meant to do. This is not specific to bitcoin or any specific algorithm, anything that can run in parallel (multiple threads) can also be expanded to run on multiple systems.
Satoshi also touched on this matter indirectly in his Email back in 2008 (before Bitcoin was launched) predicting that people will mostly run SPV clients instead of running full nodes and be mining bitcoin while it will be left to "specialized server farms" to do so.
I knew about Satoshi's 2008 e-mail, it is Satoshi, not the White Paper, not Bitcoin to be specific.
In the paper, Bitcoin is discussed and justified as a network composed of nodes incentivized to act loyally because of the rational cost/benefit assessment they could make, costs being the work and benefits being the reward, hence they are ALL mining full nodes. It is Bitcoin the way it is presented and documented, not the way it is discussed loosely by the inventor.
As of your
sharing argument:
Sharing is good, I used to be a socialist for a long time, I love sharing, but not the centralized way, I hate centralization and pools are centralized, simple.
Other than personal ambitions and judgements, there is strict mathematical reasons for avoiding centralized
sharing of computational work: Collusion resistance is linearly dependent on the cardinality of the set of actors. Once you got 3 huge players possessing like 75%+ of votes, you are doomed simply because they could easily collide, like by setting up a meeting or calling each other, couldn't they?
And there is more:
Centralized pools push miners out of the bitcoin ecosystem by enslaving them, making them work blindly on their stupid 80 bytes block header templates which point to an unknown set of transactions they have no clue about. It is literary, an alienation process by which actual miners, are kept out from the network as they have no single reason to run a full node.
Obviously it is not Bitcoin the way it was originally designed, documented, and presented in the White Paper.