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Satoshi also claimed (in an email to Mike Hearn) that Bitcoin can beat VISA with higher transaction volume and lower processing fees. Has Monero achieved this goal as well?

Bitcoin could have achieved that goal if it had been allowed to scale. Monero uses a dynamic block size so will be able to achieve the transaction throughput if usage reaches that level. Transaction fees on Monero however are limited to a few tiers in order to make it more difficult to deanonymize transactions by fee size, so without a fork in the future (which is a normal occurrence on Monero) the fees will remain higher than Visa.
Satoshi claimed a lot. For the purpose of the title the Promise was peer-to-peer permissionless transactions, with a weakness:

> public ledger cryptocurrencies have most of the characteristics of cash except one thing: Untraceability

The author argues Monero fills a missing case:

> untraceable cryptocurrency while keeping all of cash’s characteristics

One of cash's characteristics is that I can give my neighbor $1 and my net worth drops by exactly $1 and theirs goes up by that amount. There's no fee.
That's not actually true. The fee is implicit in the continuous and perpetual inflationary devaluation of the currency. Moreover, this fee applies whether you transact or not.
Inflation in not a transaction fee. At most you could call inflation a cost. You sound like you're just playing with words.
I said as much. Inflation is a holding cost. Ultimately, all costs matter, whether for holding or for transacting.
Yes

> cryptocurrencies have most of the characteristics of cash

> untraceable cryptocurrency while keeping all of cash’s characteristics
Surely this is a place where a good faith reading solves the conundrum. If the author had written, "while keeping the cash-like characteristics" we wouldn't be here and they would have made the same point they were trying to make.

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