This is something that becomes more significant when playing in the slower modes. Too many era stars depend on expansionism and war. If you spam cities, keep fighting for territory, and expand, it's easy to get stars. On the contrary, it's everything but easy to get stars with a metropolis and a diplomacy focus, be it with trading, science, or religion as a focus. Twelve stars depend on expansionism, i.e. the number of buildings/districts, the number of territories, the population, and the defeated units. It would be fine if there was something to balance it.

I'd suggest rewarding diplomacy as well. And the competitive deeds should also contribute to era star progression, not just to fame. Why not give a half or quarter star for every competitive deed? You can be first on the fame ranking, but still, reach the next era as one of the last. This is significant if you play a game mode without fame-based winning conditions, like the space race. Overachieving in one era (e.g. by delaying your era selection to build more Emblematic Districts) shouldn't be a disadvantage during the successive era(s).