I’ve heard that some schools do this to go through the process more quickly, however others I’ve heard wait until all applications have been submitted before they review them. I know that for Cornell, someone that I know who submitted their RD application in early had an interview over a week ago…
Would there be an advantage (besides stress relief 
) to submitting an application in early–to Penn in particular?
In the general case, I think there’s no advantage, but I am not certain. Understand that RD is different from rolling admissions. Whether you apply RD in August or 12/31, you’ll hear back at the same time.
For you in particular, there is certainly no advantage between submitting your application now vs right before the deadline. A few days doesn’t matter, especially when it’s holiday season and Admissions Officers are likely not reading many apps, if any, this week.