Shards seek out hosts with the potential to trigger and the temperament to use the power they would get. But obviously there's a limited number of shards looking for hosts and plenty of people considered too passive to be picked. I'd be very surprised if for every parahuman there weren't at least five people that went through roughly similar shit but didn't trigger.

How many Taylors never met their undersiders and ended up dropping out of school. How many Amys had their sisters die in their arms. How many Vistas never got an escape from their shitty home lives. Hell, how many would be brutes just died from whatever injured them.

It's important not to downplay the severity of what capes go through to trigger. Their powers don't solve their problems and getting them isn't worth the pain. Having everyone that gets hurt get a power just wouldn't work, that would be like 10% of the population. The plot necessitates triggers being rare.