The idea that Biden shouldn't run because he won't be able to answer the question "Why are you running?"

I think that's the point of this Slate article "Joe Biden’s Big Question/Why are you running?" by John Dickerson. Key paragraph:

But if Joe Biden runs, it will be a character campaign against Hillary Clinton. That doesn’t mean there won’t be specifics discussed about wages and health care and the U.S. role overseas. But at its heart what will have gotten Biden in the race and what will animate it will be character—both his own and the perception that Clinton’s isn’t strong.

And he can't come out and say that — right? — so when he's asked the inevitable question he'll have to use that story about his son's dying wish. But that's not a reason why we should vote for him. And Beau didn't tell him to get out there and destroy Hillary, but only to go ahead and pursue your decades-long dream. And that's not a reason that explains why we should vote for him — because he's always wanted it and his son, who died, backed him up. It has to be that Hillary's no good, and that will have to be his message, the message he won't be able to come out and openly admit. That's what I get from Dickerson's piece, which I read as pressuring Biden not to run.

And yet, I don't think it's obvious that Biden can't put together a campaign that's basically anti-Hillary but manages to keep a veneer of positivity constructed out of the death of Beau.