Out of pure curiosity...

[bobbin]

They invented "democracy", I find easy to imagine a rural group taking that in consideration...

Why would they give two hoots about that? Firstly most greeks didn't use it and secondly it would just be seen as another way of governing, it didn't have the conotations back then that it does today.

but I also ask myself this: the greek colonies met native population and their culture. Maybe there's a deeper reason if the native population often (not always, it's clear) assimilated greek culture and not the opposite (I think about the diffusion of the Greek language, it was a lingua franca like the more ancient akkadian language).

No deeper reason, it became the lingua franca the same way latin did in western europe, because the ruling and administrative classes of the region spoke it for a long time (from alexander to muslim or turkish conquests).

There wasn't anything inherent in greek culture that helped it spread, I should also point out that in many cases it wasn't adopted wholesale, for example Coptic (the egyptian language) was spoken by the majority of the population until after the muslim conquests.