How else is BTC miner supposed to pay for expenses?

Accordingly, is anyone who saves fiat money also economically irrational?

Actually I would say yes, they are. Once you have a reasonable cash buffer and are out of the danger-zone for random financial ruin most people should invest all excess rather than be paid a pittance for their bank to do it for them.

Yes. Which is why no one invests for the long term by amassing cash alone (fiat money). They invest it in stocks, assets, real estate, and other non-cash holdings.

The common fallacy in Bitcoin circles is that Bitcoin is the only way to keep your money safe from inflation.

In reality, inflation means that your house, your car, your stock investments, and other holdings are also worth more in dollar-denominated amounts. The only thing that becomes less valuable is cash (and fixed return investment vehicles and such).