"why did progressive politicians at the city and state level support the implementation of ballot initiatives, referendums, and recalls?

They believed that direct democracy would make government more responsive and accountable.

Explanation:

in a direct democracy, the citizens will have an active role in voting for the type of regulations that shall be passed by the government. (this is what achieved through ballot initiatives, referendums, and recalls)

Progressive politicians believed that direct democracy will give more power to the citizens to influence the future of the country. It will make the government officials become responsive and accountable because the people will more likely to not re-elect them if they do not at according to people's will.