That one is a lot more interesting, though it's basically just a map, which is atypical for flags.
The OP's flag is very abstract. Presumably, any other alien race also strives for unity and lives.
It's hard to create a better flag without actually knowing aliens and having some idea of commonalities and differences with humanity. Indeed, maybe we need a flag for humanity, not planet earth?
Well, the exact number of countries is a very messy issue and the definition of what is a country tends to be "whatever other countries acknowledge to be one". This can be especially awkward if some of the other countries don't want to accept its status and the rest plays along because they have no incentive to get involved.
That is functionally a horrible design. Imagine a couple hundred solar systems. It is very likely that one will have exactly 8 planets with their 3rd planet being their home planet. And even if such a system doesn't exist, this map doesn't stand out at all. At a glance it could represent any solar system: "Hey, this map has planets and a sun. Which solar system is that? I have no idea." This introduces unnecessary confusion and possible conflicts.
Symbolic representation of a solar system is the most generic thing you can choose about a solar system. A flag should be something unique that stands out from other ones.
Once we do colonize the solar system I'm sure invidual moons of giant planets will play a larger role than the actual planets. So I don't see this working in the future.
The only future we can truly expect, aside from total annihilation and reset of the planet, would be a total colonization of the solar system.
It's still where we as mankind originated and seems somewhat appropriate. However, maybe that's short sighted and we will get a very anti-earth separatist movement from the colonies.
But, if it is to be a "flag for planet earth", it would not need encompass colonies on other worlds, and it wouldn't be the goal of such a flag to do so. If, as someone else suggested, the right idea is a flag for humanity, then your argument works.
Seems like using a flag that gives an unknown contact your home address is a bad idea. That information might not be something we want to communicate right off the bat.
Since we are constantly broadcasting at high energy and with interesting patterns, I wouldn't worry about that. Everyone who sees this flag is either from Earth or knows its position very well.
I just read that and the Dark Forrest and that (fundamental) part of the book honestly made no sense to me. His claim that you can't locate a signal's source location was in complete conflict with everything I thought I knew about astronomy and how we locate things in space.
One suggested solution to the Fermi paradox is that any civilization that gets noisy enough to get noticed quickly gets attacked and destroyed (or taught to hide better in the future...)
The OP's flag is very abstract. Presumably, any other alien race also strives for unity and lives.
It's hard to create a better flag without actually knowing aliens and having some idea of commonalities and differences with humanity. Indeed, maybe we need a flag for humanity, not planet earth?