Is it a good idea for academics to keep track of their failures?

In the recent weeks there has been some buzz over the academic corner of the internet and social media about the "CV of failures", made public by Johannes Haushofer, assistant economics professor at Princeton. He writes:  

"Most of what I try fails, but these failures are often invisible, while the successes are visible. I have noticed that this sometimes gives others the impression that most things work out for me. As a result, they are more likely to attribute their own failures to themselves, rather than the fact that the world is stochastic, applications are crapshoots, and selection committees and referees have bad days. This CV of Failures is an attempt to balance the record and provide some perspective."

VOX picked up the story and made it larger, but Haushofer himself attributes the notion of a CV of failures to neurobiology researcher Melanie Stefan, who voiced the idea in Nature already 2010:

"So here is my suggestion. Compile an 'alternative' CV of failures. Log every unsuccessful application, refused grant proposal and rejected paper. Don't dwell on it for hours, just keep a running, up-to-date tally. If you dare — and can afford to — make it public. It will be six times as long as your normal CV. It will probably be utterly depressing at first sight. But it will remind you of the missing truths, some of the essential parts of what it means to be a scientist — and it might inspire a colleague to shake off a rejection and start again."

Many people in the academic sphere have been sharing this idea, and Haushofer's actual CoF with appreciating comments, but my reaction is a bit different. It is this: why on earth keep track of your failures at this level of granularity and meticulousness? I totally get the point that handling failures is a very important core skill of academics (as of artists and many other professional groups). I also completely emphatise with the notion that having young students and early career academics see that well established seniors have had and still have their hard time too, and that rejection is not a proof of uselessness. All hail to that! But, then again, all of this assumes that CVs of failures would be floating around without the kind of personality one would nurture by being disposed to write them up, and my reflection is about whether or not nurturing that kind of personality is a good idea for young aspiring academics, or even for academia in general. I actually don't think so, and I think our positive reactions to this piece of news of our dear colleague at Princeton, as for Stefan's original idea, have us confuse keeping track of one's failures with being open about one's attempts. 

What would be very beneficial for academic culture as a whole, as for seniors and juniors alike, were if we had a more open culture about our attempts to have acceptance (for papers, for grants, for jobs, etc.). Then our failures would be exposed too, as a side-effect, but we needn't spend energy on keeping track of them to document for the rest of the world to see. Or even focus on it, or success for that matter. The importance is the honest attempt, including the struggle to endlessly improve it. That would be a real improvement of the academic culture and landscape.