No. I'm anticipating InsaneApache mentioning Switzerland next, but Switzerland is really the exception that proves the rule. I'll explain the dynamics of why Switzerland stands apart from other democracies if anyone asks, but it's not relevant to the main argument.

Politicians serve lots of roles that are necessary for democracy. They allow citizens the freedom not to participate in elections, or at least reduce their participation to the level that they want to. Mandating universal direct democracy is exhausting, and would eventually lead to a dictatorship of the most active participants. Politicians are also better at agreeing to disagree and compromising than the average citizen, which is important in democracies. This as well as being better at taking a long term view than the average citizen, and being better at the physical act of governing.

All that aside though, the best argument in favour of politicians is the fact that every democracy on Earth has them. They are products of industrialised democracies, and the relationship is mutually beneficial - democracies gives politicos power, and they provide a whole buffet of uses for the state.