As a general comment: I've never understood how anyone could claim that the Athenian system was a democracy. To me, it always seemed to be an oligarchy with a somewhat larger olig* than other Greek states. Claiming it as a predecessor from antiquity for "democracy" is a classic case of a retroactively invented tradition.
* Yes, I know it's not a word.
I think you're making two points, which might also be considered separately.
The Athenian system was not a democracy, because it was an oligarchy. As I have argued above, there are oligarchies and oligarchies, and some of them are internally democratic, even if not equal. Or at least, they are not internally despotic. I have cited the Polish Szlachta and the English electorate as examples, because these were significant minorities of the population, comparable with the Athenian "olig" (which was not big enough to be a "poly").
I think that the existence of a democratic spirit, or some comparable sentiment, within an oligarchy is quite important. It is possible for such an oligarchy to expand until it encompasses wider sections of the population. If some of the people enjoy freedom, it is easier to extend it to others. Where no freedom exists at any level (as was the case in Russia--all were slaves, including the highest nobility) it is very difficult to introduce it into a society. But where it already exists, it is quite practicable to extend its enjoyment to parts of the population for which it was not initially designed.
Consider, for example, the
Polish Constitution of 1791
The constitution sought to supplant the prevailing anarchy fostered by some of the country's magnates with a more democratic constitutional monarchy. It introduced elements of political equality between townspeople and nobility, and placed the peasants under the protection of the government, thus mitigating the worst abuses of serfdom. It banned parliamentary institutions such as the liberum veto, which had put the Sejm at the mercy of any deputy who could revoke all the legislation that had been passed by that Sejm.
This initiative was stifled by the Partitions.
For a century subsequent to 1832, the franchise was extended in the UK, first to all male property owners, then all male householders, then all men, older women, and then younger women. But if there had not been even a restricted franchise and a representative parliament in earlier times, that process would have been impossible.
The US constitution was not designed for slaves, but once they were freed from legal servitude its protection sooner or later had to be extended to freedmen and -women, and their descendants, albeit over the course of a century of struggle.
So I think that the character of oligarchies is important, and if democracy exists within an oligarchy, that is advantageous.
Your second point
Claiming it as a predecessor from antiquity for "democracy" is a classic case of a retroactively invented tradition. is I think quite right. Although it is a "predecessor", not necessarily or even probably an inspirer, of the kinds of democratic oligarchies I have been discussing, ancient Athens is not an example of what we mean now by "democracy" in the modern states where democratic political systems prevail.