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.
The graph doesn't make much sense without a bit of explanation. (It certainly didn't to me, anyway.) The minutephysics video linked to from cptroot's comment, and also here [1] for your convenience, does a great job of that.
In short, you're right it's not surprising that the lines are log-log linear for uncontrolled growth of the virus, and that it's similar for lot of countries. What's interesting is the few (so far) cases where it drops below that log-log linear line, which indicates a containment strategy that's starting to work.
> “Lots of distributions give you straight-ish lines on a log-log plot”
I agree. I don't remember the last time I've seen a log-log plot that doesn't look linear. I've never found a lot of use in them for actually illuminating much.
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.