We are not now and never have been a democracy. Our founders crafted a republic that embodied many democratic principles. Many (most) of them LOATHED the idea of universal suffrage viewing it as nothing more than a semi-formalized mob rule. They wanted voters to be persons with a stake in their community, persons who would be impacted by the results of their selections for government offices and who would pay attention.
I actually believe that Rabbit's suggestion in the OP would have met with far more support from the founders than most of us today would expect. It was not at all uncommon for there to be property restrictions on voters in the early states (insuring that "stake in the community" quality) and the Constitution itself did NOT obviate such restrictions on the part of the several states. If I recall correctly, there was even some discussion about basing representation on number of voters rather than on population, but that this was shot down by the Southern states whose states had far fewer voters than people (especially when the enslaved population was included).
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