The 'market' itself is democratic, although this argument is typically rejected by leftists. People who spend money on goods 'vote' for the good/service to exist in society.

Also, a 'democratic market' doesn't necessarily mean that you don't have democratic processes elsewhere in the productive/distributive process of resource allocation. Firms, while worker owned, would still produce based on the demand from other individuals/firms. Imagine, for example, that Apple was a worker owned enterprise. They don't directly produce their goods, they design, brand, and market them. They still pay producers to manufacture their products, and assuming the manufacturer is worker owned, the profits are distributed amongst the workers. Profits are shared between employees at Apple who designed and distributed the goods, and profits are shared between employees at the manufacturing facility who manufactured the goods.

The democratic process, exists within the institution. Suppose a constitutional amendment was passed stating that all currently privately owned firms must be restructured such that stocks in the company are divided equally amongst employees. Given the nature of stocks, every employee has equal say in the structure and organization of the institution and what is done with profits.

If the monetary system was disintegrated, there would be severe limits on economic development, as there would be no way to increase the money supply and allow for worker owned firms to invest in other institutions.

Suppose that another amendment is passed stating that all natural resources in the geographical area of the state are owned equally by the residents of the state. A state owned institution would then extract, process, and sell the resources at a profit. These profits would then be redistributed through the state based on a democratically decided mode of redistribution (building institutions, giving citizens checks, etc.,).

What would be needed in a socialized economy, would be limits on private accumulation of capital. And anything above that limit, would be socialized.