I’m not sure what to make of this. “Lots of distributions give you straight-ish lines on a log-log plot” (http://bactra.org/weblog/491.html) so it isn’t surprising that the slopes of the lines are somewhat constant over time.

Because taking the logarithm is such an equalizing operator, I also doubt whether it is surprising that lines seem to overlap for each country. Zooming in, there still is a difference of about 20% in new cases/total reported cases between countries, even in the range of 5k-10k total confirmed cases. Taken over the course of multiple days, that can make quite a difference.