I am asking this philosophically, and not merely talking about Biden. All politicians trundle this phrase out when something goes wrong (except maybe Trump, who never took “responsibility” when things went awry).
The phrase is apparently seen as some sort of closure by the political class. However, it is not really even an acknowledgement of fault. It's not nearly as strong as saying, “I am sorry” or even “my bad”. After it is said, everyone on the politician’s side says, “See? He owned it.” No he didn’t. There are no actual consequences. He didn’t resign. He didn’t fire anyone. He didn’t offer to take a pay cut. He didn’t resolve to meet all the families of those who were lost. A few years hence, when confronted about the screwup in a political debate, the politician will absolve himself of actual responsibility for the screwup. Sometimes that even happens in the same press conference. “Look, my predecessor…”