The issue with that approach though is how do you effectively prevent reinfection of the region when all counter measures are suspended? Another carrier could reinfect the region again and all that previous work came to nothing.
It's never "nothing". For all we know (or don't), the virus might (or not) slow down spread during the warmer months in Europe and the US.
Perhaps it could be effective enough to have multiple 2-week lockdown periods (eg. separated by 2 or 4 weeks non-locked-down periods), just to slow down the spread so health care systems can keep up?
There is so many variables at play, and no simple model could come up with "the best" solution, if there ever is one.
By contact tracing, quarantine of people who are suspect, and social distancing.
Look at taiwan , singapore, hong kong, macau. You can totally slow it down to a reasonable number of new cases daily such that the hospitals can handle. Just don't start like wuhan, iran, italy...