And it’s worth remembering, Crouch was a certified madman.
But whatever Voldemort’s problems were, he wasn’t the certified madman Crouch was. He wouldn’t have let through such a plan.
To be fair, this was never my main point. However, Crouch did attempt to kill Harry in his office after the resurrection, against Voldermort’s express wishes (we can assume they were in place at the time). So Crouch could have been a tad more flamboyant than was needed.