Democracy equates to mob rule.
If you want your rights dictated to you by popular consensus, then you're a bigger fool than we give you credit for.
If we were a true democracy, every one in Hawaii would be living under laws and restrictions voted on by the states of New York, California, Pennsylvania and Illinois. Together, they represent a population almost 25M people more than Texas and Florida combined. Those six are the most heavily populated in the US.
When you ask for Democracy at the Federal level, you are necessarily relinquishing democratic rule at the state level. Because, to do so would mean ripping up the Constitution and vacating the Representative Democracy (Republic) we have had for more than 200 years.
p.s. Socrates died a very long time before the US and our "great experiment" ever existed. In fact, he was born some 470 years before Christ. Add another 2000+ years to that, and I'm not so sure we should be following what he said about political ideologies and applying them 2500 years later.