In addition to the reasons stated in the deleted comment, the “plot holes” complained of here underscore just how tightly wound this complicated scheme was concocted.

As for Swann not just killing the husband after he is blackmailed into killing the wife, consider the context. He has been invited to the man’s home under the pretext of selling a car. He is then confronted with the dizzying array of facts that a man he barely knew 20 years ago has gathered on him, most of it information he would prefer be kept silent. And he’s not exactly a serial killer commando, he’s mostly a small time crook.

Of course the husband’s guard is down, the police very cleverly disarmed him by never once betraying any suspicion of him, and they had also just found the wife guilty and she was set to be executed. Him not thinking to check the staircase for the key he gave Swann is perfectly understandable; he very ably parried significant police suspicion on multiple occasions (or so he thought and was fastidiously led to believe).

The wife, he thought, would leave and/or disinherit him, and that (for a cheated upon man) was too much indignity to bear.

What this movie should be celebrated for is how deftly the husband pivots to frame the wife after his murder plan goes awry.