That’s a tax on the poor
“Pay” is doing a lot of work there. My house is half equity half debt. The debt gets to be paid off with inflated dollars. And I pay no capital gains on the appreciation. I can, however, tap it for liquidity if I need it.
Classically, yes, particularly when that wealth is closer to productive capital. In modern economies, the rich also hold a lot of debt, which lets them benefit from inflation.