A gold standard also solves inflation, but fundamentally and non-policically, by limiting money to the supply of gold.
The purpose of the Fed is to inflate the money supply for the benefit of the government, the banks, and borrowers who want artificially low interest rates at the expense of everyone else who uses money. If the Fed did not inflate, it would be no different from a gold standard, and in fact, when the Fed corrects inflation, it does so by reducing the production of new money as under a gold standard.
That’s not how I define inflation, and I don’t think it’s how most people (even economists) define it. I define inflation as stuff getting more expensive.
If you define “inflation” as “increase in the money supply” and “value” as “value denominated in the mass of shiny rocks”, then yes, a gold standard prevents inflation and stabilizes the value of money. But this is a tautology, not an argument.