'Cryptocurrencies are such a puzzle because they violate all the rules of a medium of exchange'.

The usually considered 'rules' (or fundamental requirements) are that a monetary system provides MoE, SoV and a unit of account.

Bitcoin provides all these although unit of account is difficult where Bitcoin price relative to goods and services is volatile. Bitcoins MoE ability is also compromised mostly by the direct and sly obstructions put in place by the legacy fiat operators- tax reporting/collecting requirements and threats from banks to close businesses fiat banking if they accept Bitcoin...under the pretext of KYC/AML.

Bitcoin certainly does not violate all the rules- as it is far superior in SoV, adequate(bar obstruction) in MoE especially with LN and being inherently digital/online Bitcoin has advantages in terms of MoE use online and globally compared to fiats antiquated, inefficient and expensive payments/settlement channels, and even unit of account viability will improve as Bitcoins relative value becomes more stable as it logically will as market value increases.