It is really not a matter of comforting everyone with the knowledge of the cause. It is more a matter of how to make precise changes in order to mitigate future accidents. There is a cost benefit study done on every proposed rule change in the US. These efforts can be interminable due to industry/authorities argument over both cost and benefit. The benefit argument is dramatically strengthened by precise knowledge of previous accidents. When that knowledge is less precise, as in no recorders, the argument can be fruitless.
Following the Roselawn accident in 1994 we had over one hundred DFDR parameters downloaded within a couple of days. We had 80% of the knowledge we needed to reach some preliminary conclusions within a week. Subsequent rulemaking efforts have benefitted greatly from the comprehensive and specific data yielded in this investigation as well as that of Monroe, Michigan in 1997.
Contrast that with TWA 800...in this case, all we had from the recorders was a very specific point in time when they ceased recording. That in itself was useful in validating the breakup sequence, but the rest of the work had to be done by careful reconstruction and analysis. Fortunately, thanks to the impeccable work of a group of young Navy divers who remain largely unrecognized, we were able to do that. But the process was enormously expensive, painstaking, and remains controversial to the public. Independent power sources for those old recorders would have made a very large difference, not only in public perception, but in the dynamics of subsequent rulemaking in areas like fuel tank inerting and fuel tank safety analysis.
If you want to get a serious change made following an accident, you'd better be able to build an argument that the beancounters cannot squirm out of (and squirming tends to come naturally to them). Good recorder data can do that.