There is an old discussion at Show satellites and time elapsed in geopoint dialog that gets into the weeds on this topic.
I haven't been a fan of averaging, but @Ivangayton emailed me a few days back and that changed my mind. He said,
Averaging is still used a lot in professional surveying (expensive Trimble and Leica GPS units often use some form of point averaging, and a lot of formal surveying contracts actually specify the number of points that must be collected at a single location to be considered a valid point), and there's good evidence for some slightly more sophisticated algorithms. Fuzzy averaging is one, 50% radius is another, and there are a few more out there.
Bottom line: I don't suggest that averaging should be mandatory, nor should it be presented as a sure answer to precision and accuracy concerns. However, I do think that it's a nice option to offer users, as those with the sophistication to understand the pros and cons of averaging will likely be happy to have the option open to them.
If folks want averaging, so be it, but I think it should be opt-in, the algorithm needs to be specified, and the documentation needs to be clear about what it is and isn't.