Not 'every company of a certain size', all of the means of production would be worker owned. In practice what this would mean is that if you run a business you can't continue to extract profit from workers without compensating them or allowing them a collective voice in what the profits are used for. Whether they want to run that as a co-op (which can include consumers and not just workers, eg REI) is up to them. There isn't a central government directing this under communism, as the eventual goal is for the state to no longer be necessary. I think that part is unlikely to happen naturally and communists are pretty vague about it IME, I'm more of the opinion that capitalism needs to be legislated out of existence and kept that way with a strong government. But implementing more widespread adoption of worker-owned companies is going to be necessary if we want to get out of this goddamned mess, because letting one guy (or a board of guys) decide what quality of life tens of thousands of people have clearly isn't working.

I don't believe the owners of a company should be compensated, because they've already been vastly overcompensated by the wealth they extracted from the workers and they should count themselves lucky if they're not in an Ayn Rand situation afterwards. Because the thing is, if you're actually wanting to do something cool, you don't care if it's going to make you rich as long as it's not tanking the company. Think about how many scientists, engineers, artists, etc have been held back or had incredible projects canceled because some CEO decided that x% profit on it wasn't a good enough return. Do you imagine that would happen with nearly as much frequency if, say, the organization was entirely owned and run by the highly skilled professionals actually doing the work and interested in it?