Odds of Getting In
Now, just because any Tom, Dick, or Harry can run for office doesn't mean they'll get elected. Telling people to vote for you is one thing; getting them to vote for you is a different thing entirely. Thus, we have the most American of political ideas: the campaign. For the past 200-plus years, Americans have held "bloodless revolutions" every year to elect leaders to every level of government. This process is messy and occasionally confusing, but when the dust settles, whoever has the most votes wins.
So what does that mean? That means to get votes, you need supporters. You need people who can go from house to house explaining your ideas or can stand on street corners holding a placard with your name on it as cars honk in support or anger. You may be the mayor of New York City, but come election time, you still only get one vote unless you earn the others. So start polishing those debate skills and get ready to begin your charm offensive.
There's also, of course, an incredible amount of money in politics. Just as with the federal and state level, local politics often requires a cache of cold hard cash to get the attention of those hearts and minds you so desperately want to win over.