The big practical obstacle to this is that the things this flags people as potentially committing fraud based on look to be the same things an actual fraudster

The big practical obstacle to this is that the things this flags people as potentially committing fraud based on look to be the same things an actual fraudster would manipulate in order to get payments they're not actually entitled to - stuff line income, living situation, kids etc. So the obvious route to not setting off fraud alarms would likely involve not committing fraud, or at least not the most obvious and profitable kinds.