The cops are going to be searching a lot of grannies.
Unfortunatly you have nailed a principle reason for not profiling. What is needed is for a change of fashion. Only tight fitting clothes (men and women) and no bags, or purses, unless small and transparant.
The other solution is to get lots of those low power xrays and scan everyone. (Shoot to kill when a bomb is discovered.) And fortet the so called privacy issue, people will be more modestly covered than in a doctor's office, and the scan will not take permanent photos. BTW, keep these scans secret and the location of the scanners secret. Deploy them with the troops as well as any crowded likely terrorist spot. The terrorists will start turning up dead and no one will know why.