It is a very good point that we cannot, and should not, introduce anachronistic ideas fully-formed into a Classical context. For one thing, we need to keep in mind that the people we are playing think very differently from how we do. If we advance a stirring argument in favour of representative democracy and the values of citizenship, they will agree; whilst taking a completely different meaning from it than we would. Equally though, we can make changes, and indeed, we already have done.
Look at Eretria today, her extremely developed and yet accountable state institutions, her virtual absence of slavery by the standards of the period, and the large proportion of Metics and freemen and the encouragement of more. All of these are remarkable to a greater or lesser degree by the standards of Greek poleis from the time period, especially how developed our government institutions are. Even the status of women in Eretria is somewhat remarkable, although maybe less so compared to some other cities.
The important thing is how these changes came about; taking place within the historical context, and for reasons that made sense within that context.
Think about it a little like the evolution of the eye. Complex machinery does just not arrive on the scene suddenly, fully formed. The odds against that are more than astronomical. Instead, you see a series of iterative developments, each selected for in the context they took place, with no overriding design, which come together to build an eye over time. First, because it is immediately advantageous, an animal gains a spot with some light-sensitive cells, allowing it tell between "light", and "dark". Then, this spot develops into a pit with some allowing the resolution of very crude shapes, because that also makes immediate sense within the context it happens. And so on.
So too with historical institutions, a lot of the time*.
This means that we can absolutely make changes, and perhaps end up with an Eretrian state or culture that looks very different from what came before! But each departure, each change, each innovation, each step of our evolution, has to make sense within the context of Antiquity and Classical Greece, and the context of Eretria. We cannot time-warp our own ideas fully formed into the minds of our characters; any new idea has to make sense to them, in their context, as they would think of it, based upon their reasons, motivations, and metaphors for understanding the world. To a large extent, events rather than any kind of grand design are going to drive this process.
Like a rider sitting balanced atop a log in a fast-flowing torrent, what we have is the option to tilt and nudge, perhaps altering our course in the process, although we cannot see past the next bend in the river.
So long as we don't fall off, of course.
*(There are exceptions to this, of course, because humans are intelligent and far more complicated, and will often try complex designs, and so history is complicated. Helpfully, the times when people have attempted to introduce complicated designed systems ex-nihlio on an unsuspecting populace can often be easily identified by looking for the Wikipedia articles that contain an "estimated death toll" column.)
