Since Japan is not an autocracy, politicians are actually vulnerable people. Scandals may end their career. Only a few politicians have what it takes to turn scandals into a strength, like Trump, for example. But then again, this is a delinquent manga, so nothing needs to make sense. A random politician can have as much unchecked power as a developing country dictator, without explanations. Just like the police doesn't exist in delinquent manga, unless it's needed for a specific arc, after which it again stops to exist.