Yes, that was the exact system for years, and that’s how it still is in every other race besides US President now. Anyone with enough support can get on the California Ballot (with the parties generally being Democratic, Republican, Libertarian, Green, Peace and Freedom, and American Independent).
The California Constitution (the longest in the world) also has clause that means Californians vote on what Amendments to add to the Constitution. These are called Propositions, and we generally vote on 6-15 in every general election.
We vote in all judges, city officials, school officials, water officials, and other positions.
California elections are based on the top 2 system. Top 2 candidates in the primary advance to the general election regardless of party affiliation (except for US President). For example, the last Senate seat election came down to 2 democrats.
We also have “recall” elections. It’s like being impeached by the people in a sense. If enough people provide signatures for a recall (somewhere above 1,000,000), then one can take place.
So, I consider California to be the most democratic place in the world (or at least one of the most).