The false positive rate with home alarms is not the same as that of acoustic gunshot detection alarms. Your cat will routinely set off your interior motion sensor alarm; a loose door fitting will do the same to the front door.

If criminals want to use gunshot noise to scramble police presence to a specific area, they can obviously do that without gunshot detectors. The point of detectors is to make it easier to follow up on ideopathic gunshots.