Any argument that pre-flight screening in the crew room, or wherever, out of the public eye does not guarantee 100% interception of incapacity is a weak argument.
But then, nothing in life is 100% guaranteed.
Such a system can be implemented and eventually will be, despite all protestation, not because it will be 100% effective but because it is more effective than the current honesty-box system and because the paying passengers will come to expect it.
100% pre-flight alcohol screening is already the law in India, for all pilots & cabin crew, before each flight segment.
Personally I believe such policy is excessive and not based on sound risk analysis. But it is, as you say, a policy based on public expectations.