The question can be answered in more than one way. One is to appeal to the current Japanese rules, under which bent four is dead because the defender has no effective ko threat. The defender has no effective ko threat because the only threat is a pass for that specific ko, after which the attacker will win the ko. Another is to address the reasons that the current rules are as they are. That is more speculative.
The current Japanese rules make explicit what has been implicit in the rules, namely virtual play after the end of regular play. Dead stones are removed without actual play, but may be removed by virtual play. The play is virtual because, if the defender is allowed to pass without penalty, the attacker loses points by capturing dead stones. Under virtual play Black, the attacker in this example, could remove the White ko threats before playing the bent four. Then Black could win the ko and capture the White stones. Since Black could do that, the White stones are dead, and may be removed without actual play.
Now, on rare occasions White may have an irremovable ko threat. In that case Black cannot remove the threat through virtual play, and, under current Chinese rules this bent four would be seki. However, back in the mists of time the Japanese decided that bent four was simply dead. Perhaps they were unaware of the rare occasions that there would be a bent four and an unremovable ko threat, or perhaps they felt that accommodating such rare positions made the rules unworkable or unappealing.
I have added a couple of comments and illustrative variations to the SGF file.
Edit: Even though under area scoring, which the Chinese rules have used for centuries, Bent Four is not necessarily dead, there is some evidence that it was considered dead under earlier Chinese rules, because there are ancient Chinese life and death problems where Bent Four is treated as dead.
