There is no general 'simplification of tenses'. It is simply that, when we talk about past events, we often do not use the past perfect if the sequence of those events is clear. In the first of the examples below, the past perfect is necessary to show the sequence of events; in the second, it is not.
When I arrived she had already left.
She left after I (had) arrived.
Similarly, if the verb itself contains the idea of completion, then a perfect form is not essential.
You can leave when you finish/have finished your homework.