It doesn’t work because the entire system above it takes massive amounts of private money, which influence downballot races.

The parties spend a lot of money to raise the profile of a few candidates in a state (people can only remember a few names anyway), then leverage their popularity to endorse candidates in downballot races.

In practice, whatever local candidates supported by the largest party-sponsored get-out-the-vote operation wins. In NYC, that means a figurehead celebrity mayor and most of the lower positions filled by a political machine.

Well what are you going to do, give out the tens of thousands to anyone who shows up and fills out a form to run for office? There has to be a minimum threshold for the relevant managing agency to determine which candidates are serious. Meeting that minimum takes money and influence.