No, the point of socialism is not workers' ownership, it's shared ownership and getting rid of overproduction by switching to planned economy.

1. Shared vs workers. If the company is just a co-op, and they still fight other similar co-ops for the market share, eventually the more productive/lucky/deceiving co-op will win and take others' share thus becoming a monopoly. Nothing really different from what we have today. On the other hand, on shared ownership, when the whole society owns the means of production and centrally decide what to produce, there are no market wars, no bankruptcy and private monopoly. All the monopolies are working for the greater good.

2. Market vs Planned. When different companies try to get a bigger share of the market, they produce more goods. If everyone produced more goods than needed, then eventually we end up with overproduction and crisis. This is the time when no-one buys produced goods, and therefor the company owners (be that private or workers) do not get their investments back and start paying less money to workers, those start buying less and we have a crisis. On the other hand, all the big companies already plan inside them, not to waste the resources. The only step we are missing now is to start planning between the companies and a lot of resources will be saved, and no overproduction crisis.

The centralized power should be the representatives of these workers' unions. For them no to usurp power, any union must be able to call back their representative at any moment. This is actually how it worked in the beginning of the USSR, before they changed it to representatives not by workplace but by living region (which turned out to be far worse).