Anyone who thinks that the RE agent's list of names at an open for inspection will be followed up by the police in the event of a burglary is living in a fairy land and/or has not many burglaries. Police do not investigate burglaries, they give police report numbers for your insurance.
Further, the vast majority of insurers won't cover theft when the criminal was invited into the home. It doesn't matter if you can give the insurer the name, DOB, address, photograph, passport number and fingerprints of the offender. Even in the extremely unlikely chance that the thief/burglar was caught and convicted (you would be better off betting money on the horses), you aren't going to get any of your property or money back from the criminal, and they probably won't go to jail, so taking details is completely pointless unless you are going to get 100 points of ID and do a police check.
If an agent insists on taking people's details at an open inspection it is for their own reasons, and nothing to do with the home owner's interests (though they might be presenting it in this way to the home owner). If someone wants to protect their home from criminals then do not have opens and have the agent screen each buyer to ensure (as much as reasonably possible) that they are legitimate. At the very least, criminals at a private inspection will know that the RE agent may remember them after they have pulled off the same stunt a few times, and send them packing.