I'd guess this type of screening only works because we're currently very bad at programming cells. Checking whether a DNA sequence is malicious can't be simpler than checking that a computer program is malicious. And we all know how well that works.
It's arguably easier to check for malicious DNA than malicious computer programs. The motifs for pathogens are pretty common. It's also highly unlikely that someone will create something totally novel, and the experiments required to test malicious properties of a bioagent would be somewhat detectable.