Why doesn't Bitcoin solve double-spending with a central "mint" that checks every transaction?

A mint would work, but it just recreates a bank — the entire money system would depend on the one company running it, with every transaction forced through them.

In a mint model, a coin is returned to the mint after each transaction and reissued, so only mint-issued coins are trusted unspent. But that is a single point of trust, failure, and control — exactly what peer-to-peer cash exists to remove.

The requirement instead: let the payee confirm there was no earlier spend without any trusted party. That means all transactions must be public, and participants need a way to agree on a single history of the order they arrived in.

This isn't hypothetical: pre-Bitcoin digital cash such as David Chaum's DigiCash / ecash (1990s) worked much like a mint — cryptographically clever, but issued and cleared by one company, and it went bankrupt. Bitcoin's whole design aims at cash's finality without that central issuer.

Go deeper:

• ecash (David Chaum / DigiCash) — Wikipedia — the best-known pre-Bitcoin digital cash, centrally issued by a single company: exactly the mint model Bitcoin set out to remove.