Variation in drop dates, and effect on student outcomes
I'm not personally aware of formal studies on the subject, but at my undergraduate institution there was a carefully thought policy that seemed to work fairly well.  They had not one, but two different drop dates for classes, with different intentions:


The first drop date, ~5 weeks in, left no record at all, and was intended to allow "class shopping" and academic risk taking. This made registration a low-stakes decision. A student unsure whether they could handle a hard class or undecided between two classes could simply sign up, try things out, and then make a decision after a couple of weeks, before investing too much.
The second drop date, ~12 weeks in, left a record on the internal transcript, and was intended to allow a failing student to triage and focus on their remaining classes.  It still didn't show up on external transcripts (except as a light-load semester).


With these two dates as long-standing and well-accepted policies, professors tended to include them in their planning.  Most of the early "shopping" drops happened in the first week, so professors tended to wait until the second week before doing things like arranging tutorial sections or setting presentation schedules.  

Similarly, grading policies mostly tended to assume that D, F, and late drops were synonymous.  Thus, many classes set their first quiz before the first drop date, to let students have their first serious assessment of their progress before that decision deadline.  Likewise, curves were often set to assume the worst grades would have gone to the students who dropped, meaning that students who stuck out the class were not unfairly penalized (though they could still fail if they did that badly).

These policies I'm sure do create some statistical GPA inflation, but I doubt it has much significance because 1) it would not generally affect the stronger students, and 2) significant failures are still visible as gaps on a transcript.