Disclaimer: I work at IMVU, but I am not the article's author This is a problem you have to solve for your own context. I suggest starting with only the biggest problems, and seeing how the process works for you. You'll see the people who are in those meetings getting accolades for their follow-up work, and you'll find that as the root cause analysis gets up to why #3, the participants are solving problems they didn't cause. Both of these will help to build the right corporate culture, as you mention. Then, if it seems appropriate, it will be easier to apply 5Ys to less serious problems, because their value will be well-known to the team.
Being mentioned in a 5Y here never bothered anyone. Because you know you have to come up with a fix for all five levels, everyone too preoccupied thinking up solutions to begrudge anyone.