Honor system? Then it won’t work. We will remain vulnerable to whatever high transmission variant comes in on the next airplane.
In the case of Delta, it’s already here. About 6% of cases in the US. For Britain, it took about 5 weeks to go from 6% to being the dominant variant.
So, mid summer, it will be dominant. By late fall, the seasonality kicks in and we find out which states got their act together and which did not.
Since covid has only been recognized for about 18 months now, I'm not convinced that it has a true seasonal component. Arguments for a seasonal effect include the US peak in January/February and Australia in August, but South Africa's caseload peaked in October and Argentina's numbers just wander all over the place inconclusively.

If the pandemic roars back at us next winter, I caution that it might be with variants that have evolved to survive the current vaccines.