I think of "five whys" more as an example than an actual methodology. The goal in my opinion is:
1. Dig into the root causes. Five Whys is at least helpful in giving the idea that the root causes may be several layers away; you should definitely go past 1 or 2. Untrained humans find it very cognitively tempting to stop at exactly 1; this must be overcome and the Five Whys meme is a good entry point for that.
2. Don't be stuck on Five Whys literally, as essentially a linked list of exactly length five. Causes can be trees. (I mean, technically nothing stops them from being full graphs, at least from a high-level view that ignores temporal dependencies, but generally you need to tree-ify them for this discussion or you'll literally loop around the graph in your postmortem and analysis steps just like a computer would!) A 5-element linked list is merely a particular shape it can have. Management encouraging "Five Whys"-like thinking is a good thing; management mandating that an incident come with a Five Whys analysis with exactly five whys in a linked list would be missing the point in that oh-so-classic management methodology way.
3. Once you have your root cause tree, you examine it with the same engineering/business cost/benefit eyes as everything else. "The entire company's organization is inimical to this sort of quality" may be true, but extremely expensive to fix on its own terms. Even more so when you look up and consider that the company may in fact have other good reasons to be organized that way; there is no perfect organization that solves all problems optimally, and it may be a net loss to even consider re-orging the company to solve one particular thing that in the global context is an annoyance, if it would in the process break the organization that is producing actual value. But you may find a process tweak in some other layer that will mitigate 80% of the problem for hardly more than the cost of a meeting. It is perfectly valid to come up with a portfolio of solutions; one pattern I end up seeing a lot is the cheap short-term bandaid and the longer term fix. Cynicism aside, yes we often do end up with the long term fixes getting put into place... the key there is that they are usually themselves a portfolio of other fixes we needed that long-term fix for, not just this one issue that we've put a bandaid over.
I'm yet to ever participate in an analysis like this that didn't produce some good actionable item. Often at least one of them is indeed quite cheap, even if fixing the root causes is expensive.