The point is that the Jedi are not politicians. They're keepers of the peace. It is the job of the Senate to make or break policy and it is the duty of the Jedi to help when necessary. The Jedi were not created to be a political institution. There's local security which Anakin feels was more than sufficient to handle protection from assassination attempts and then there's the Jedi which goes beyond that. The Jedi are the FBI to the Republic. Except for the Republic during the war. Yes, local armies. But those are for individual worlds. The Senate needs to approve of the Military Creation Act, which would then be used to create a massive army from those smaller security forces. This is why during the Clone Wars, the Jedi and the Clone Army were assisted by warriors like the Gungan Army and resistance fighters like Saw Gerrera who lead the Onderon resistance and Cham Syndulla, who lead the Twi'lek's on Ryloth. The Jedi could help the Twi'lek's, but they would be severely overpowered against the Droid Army. But with the Clonetroopers, they were able to make a difference. In fact, that was Palpatine's whole political campaign. He would be a strong leader who would cut through all the red tape and get things done. This is why the people started to cheer him on when he was given Emergency Powers and additional executive powers, because he was able to bypass the Senate and make decisions such as where and when things are done.