There was a time where “pooled” testing was done. When there was not enough testing reagents they would mix a bunch together to run in the lab as a pool and if a single test was positive then the pool could be sub tested. I don’t think they would just call everyone positive but would then retest all the members of the pool. That is the pooled testing concept...government execution may vary.

Ps worked better in fixed locations like nursing homes or during hard lockdowns in large apartment buildings etc