Of course it's destructive to the average person / taxpayer, but who cares about them? Nobody does who's in charge, that's for sure.
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.
Inflation makes the past matter less. It erodes both the wealth of the super-rich and the debt of everyone else (the farmers who had to mortgage their farms in 1896; the normal family now who has a home mortgage as the norm). That's very attractive to a lot of people, not just those managing the national debt.