And on some paths he does, and will.
However in the Brainwashed path, Zach being smart is very deliberate. It is a counterpoint to the sexist stereotype that men are idiots. It's also very plausible, because he's had time to think this plan through, and from watching true crime videos, he has a good enough idea of what not to do.
However there is a subtext that I think you missed. A big reason why Zach's plan is successful is because there are way bigger problems that what he's doing. A nearly empty office building. A security guard who doesn't really give a shit, and the fact that he was able to acquire a Re Education helmet at all.