Profiling actually does work in your scenario, in the sense that it makes it one step harder for the bad guys to succeed. It is much harder for terrorist groups to recruit agents, particularly suicide agents, outside of their core ideological group. How many native-born Scandinavians are going to be willing to blow themselves up, let alone pregnant ones? Same kind of thing with native-born Americans and Western Europeans outside of the recent wave of radicalization-prone immigrants. There's just not the cultural acceptance of doing such actions.

Because it's harder for the bad guys to recruit in these areas, it is that much harder for them to put together a successful operation. They have to trade-off potential loyalty and skillset issues with these "innocent looking" recruits vs. using their core of highly-motivated better-trained suicidal young men.

I'm not necessarily supporting racial/ethnic profiling, though I do believe it would be much more effective than most people are willing to admit.

But the real problem in this specific case isn't profiling, it's the typical DHS reaction of massively overreacting to a relatively isolated incident. E.g., a few fake or actual pregnant women blow themselves up in countries that are generally warzones, and DHS starts treating pregnant women in Minnesota as the greatest threat since Osama himself. Think I'm exaggerating? How about when a half-baked ill-conceived impractical plot to use liquid explosives on transatlantic flights resulted in an immediate worldwide ban on an entire state of matter as carry-on baggage? There was never a domestic US threat, and didn't seem to be any credible/current threat after the initial half-baked plot was busted. But that didn't stop the massive overreaction. Same concept with the shoe thing.