I think you may have this flipped.

Inflation is, more than anything else, a tax on cash (and last time I checked, your average person didn't have a whole lot of cash on hand). Practically speaking, it helps debtors at the expense of creditors by shrinking the value of liabilities on the books.

The debt hysteria we see isn't because the elite don't care enough about inflation - it's because the costs of it fall more heavily on those who write big checks to political campaigns.