I understand what you are claiming, but it's a narrative not based on what actually happened.
The places that locked down earlier stayed locked down, and the places that locked down later re-opened earlier. No state stayed locked down to "dig themselves out of a hole"; that's not how any of the waves played out.
Whole countries locked down earlier, cutting the waves and death count to negligible numbers. They opened up in summer 2020, but later closed early again.
The places that locked down earlier stayed locked down, and the places that locked down later re-opened earlier. No state stayed locked down to "dig themselves out of a hole"; that's not how any of the waves played out.