Doesn't it make sense to do exactly this? Once your population reaches MAX VAX (tm) you let everybody get the variant that you still have solid protection again

Doesn't it make sense to do exactly this? Once your population reaches MAX VAX (tm) you let everybody get the variant that you still have solid protection against. They then get natural immunity to the latest and greatest. Herd immunity achieved going into the winter. The future variants (Delta+++) will probably have full escape ability against the almost 2 year old vaccine. But they will be much closer to the current Delta. Thus widespread boosted natural immunity will help carry the load as these new variants emerge. By the time the Delta-based booster gets produced, it will be too late.