No he didn't (unless you can find a quote from the white paper that makes this claim).
I already posted this two pages ago, but in case you forgot,
The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions...
A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem... What is needed is an electronic payment system based on cryptographic proof instead of trust
The purpose of Bitcoin was
supposed to be reducing the cost of small transactions.
So why did it fail? Because it wasn't
actually about reducing small transaction costs, it was a libertarian's answer to 'worthless' fiat constantly being 'debased' by 'printing money'. Bitcoin couldn't be a part of that, so its inventor created 'digital gold' which had to be 'mined' and had a strictly limited supply. Furthermore it was designed so that the computing cost of 'mining' would
artificially increase as more 'mining' was done.
There was no good reason for this 'digital gold' idea to be a part of the scheme. The obvious result of the limited supply and increasing mining cost was that the value of each Bitcoin would have to increase as the total value of transactions in the system increased - IOW it was highly deflationary. This is a deliberate choice that 'Nakamoto' made to fulfill his
real goal, which was to replace that debased fiat with money that retained its value. Why would he want that? Because libertarians are selfish pricks who think their wealth should increase all by itself without them having to do anything.
Of course this meant it would soon attract the attention of speculators, who would throw far more money into the pot than was needed for those 'small casual transactions'. This would blow up the price even more and create an 'arms race' of miners making more and more powerful computers using more and more electricity, a possibility that I'm pretty sure 'Nakamoto' never considered. He probably thought that everyone would just use their personal computers to mine Bitcoins in the background. Typical libertarian naivity.