Is a roof overhang necessary to protect the facade?

Was it just the color or what else did you do to make it work without an eaves overhang?

We didn't do anything else. We had a facade paint from Keim; I can check if you're interested to see exactly which one it was. At our neighbors' place, the facade on the weather side at the gable was at most half a meter just below the eaves still white and thus protected, the rest was, as mentioned, spotty and black after a few years; especially after rain it looked bad.

What would be the minimum in your opinion?

~Protection from rain without wind is probably already achieved at 20cm, but how often do you have that? And at that point, I would also consider the aesthetics. A 20cm roof overhang looks very stubby. I find our 40cm plus about 10cm from the verge tile much more harmonious

mainly flat roofs, because we found few gable roofs without eaves, inspected them, and most had dirty facades where you could see that water ran down the wall and also partially into the wall.

Yes, that's because the dirt actually runs directly down the facade from the parapet.

standard 70-80 cm eaves.

That is actually not standard. Anything above 50 cm is, by the way, added to the floor area ratio, which alone is why it is not standard.
Normal or standard dimensions – I still believe I remember – are 30 cm on the eaves side, 40 cm on the gable side.
Therefore, these dirty water streaks cannot be caused by the eaves.

And of course, the appearance plays a role. There is the barn aesthetic, where eaves are explicitly omitted, which can be nicely realized with a wooden facade or clinker brick.
Furthermore, eaves can regulate or negatively affect the sunlight entering through the windows. Two-story urban villas with too large eaves let less sun into the rooms on the upper floor, and it can look like an oversized mushroom cap.