Covid testing is a little like an MoT test - only valid at the time it is done. Two minutes, two days, or two months later it is proof only that the test was passed previously.
Controlling the virus is about reducing risk (like checking MoT history before buying a car). It is very simple - social interaction spreads the virus. Reducing interaction and the probability of an individual carrying the virus will reduce the spread.
So the only real questions are (a) whether the benefit from a test is more or less than the risk, and (b) is the proposal feasible.
Testing all who visit a care home may be proportional and feasible. Testing all who to Tescos may be feasible (testing capacity aside) but most would regard as an over-reaction.
Assuming a 24 hour validity for a test is far better than no test. With no test (simplistically) one may have contracted the virus at any time in the preceding 14 days and be infectious.
A negative test within the previous 24 hours means that you may have contracted the cirus only in the preceding day.
What this means in terms of risk reduction depends (I assume) on whether infectivity varies within the 14 day period. At a guess a 24 hour test validity would reduce the probability of infection by 13/14th - approx 93%.
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