but through businesses taking loans.

... Also called "printing money".

The classic inflation from the economy working a little too well is not a flat tax, since both wages and prices are growing

Inflation doesn't cause wages to grow proportionally, despite what some Harvard wankers like to pretend. Theoretical models are interesting in science, but for something like economy, they are completely useless.

Classic inflation erodes the savings of the rich, and erodes the debts of the poor.

Capital ROI is almost always greater than inflation, meaning wealth inequality increases regardless of inflation. This is before taking into account that physical assets (e.g. housing) also increase in value through inflation, meaning the owning class never loses money to inflation.

Again, theory and practice diverge pretty much entirely.

Inflation is a concept created by governments to be able to run on a perpetual deficit (necessary when you privatise everything profitable by selling it to your buddies). Making a tax on the poor is a "nice" benefit, but don't be mistaken: if the owning class saw it as a threat to their wealth we'd be back to the gold standard already.