There is a Latin sentence we use to describe a certain fallacy: Post hoc ergo propter hoc. The English translation is simple: After this, therefore because of this. The post hoc fallacy retains its Latin phrasing even in English, which might suggest that we as a culture have been referencing this fallacy continuously since the days when all educated men understood Latin.
We're not required to use Latin. It is just as sensible to describe the fallacy in this way: Timing does not entail causality. True, but it implies it*, or at the very least suggests it.
The word "since" has been influenced by that implication. Sometimes it means something like "after". Sometimes it means something like "because". Sometimes it is difficult to know which meaning applies.
I have not written to her since my brother died.
To my eye, this "since" is about timing. The past indefinite "died" establishes a historical event. You have not written to her after that point in history.
I have not written to her since my brother has died.
To my eye, this "since" is about causality. The present perfect "has died" establishes an existing state of being. You have not written to her, and his being dead is the reason.
My eye notices this distinction, but I do not expect every native reader's eye to see the same. The difference in grammar between these two sentences does not entail a division in interpretation. Given an appropriate context, either sentence could express causality, just as either sentence could express timing. Both sentences imply both interpretations. You as a reader must choose which implication to dismiss, if you choose to dismiss either implication at all.
* The post hoc fallacy deserves its fancy name and its centuries-long discussion because it is ridiculously easy to mistake implication for entailment.