If Cleveland had its own currency, you could derive globally applicable lessons. But it doesn't.

The "normal way" is much much better than deflationary expenditure cutting. Deflation increases the debt burden in real terms.

The underlying reason governments are following austerity is because protecting old people's benefits & pensions (the people on the credit side of the debt, i.e. claims on future production) is more important than growing the economy for young people, because that's how the votes are structured in the economies that matter (Germany in Europe). Politics and demographics are pro-austerity, not economists.