As long as you have a market dominated economy whatever goverment you have will become controlled by that market. They got the money they got the power.

Also, even if you could control corps, markets are inefficient anyways, they waste insane resources on useless advertising, often spend multiple times the resources on doing the same RnD simply due to being separate entities, make useless copy products only differenciated by brand, and they are inefficient from an information stand point too. For example company A knows some economic information which would provide more value if shared with the entire market/society than if it kept it private. The result will be that it will keep it private in order to maximize private profit. This is the issue with the profit motive, no matter what regulations you slap on it it will always optimize for self maximization not societal. An amazing example of this is oil companies finding out about climate change and not telling anyone. The slave labor example you gave is another example of the fundamental issues with markets. Attempting to patch up a fundamentally broken system is a fools errand.

The better alternative is a planned economy, and yes they do work, the idea that they are inefficient, never innovate, and never work is cold war propoganda easily contradicted by the fact that the USSR was the world's second largest economy, a world superpower, sent the first man and satellite to space, first spacecraft on the moon and another planet. This was all after having gone through ww2 most of their industry destroyed, 20% of men killed, and being cut off from international trade. Yes they did go through famines and then they ended those famines for the first time in the region's history. All this in additon to lacking modern communication and computational technology rather having to use mechanical calculators. History, as much as propoganda would like it to be otherwise, is clear.

Today with our modern technology could easily have a planned economy superior to any economy planned or market of past. For example, supply chain issues often are only delt with one market actor at a time, only responding once the problem hits them leading to disorganized and uncoordinated responses. In contrast a planned economy can detect such an issue and communicate to each factory or warehouse etc in parallel. It's basically like vertically integrating the entire economy. It would also allow us to far more easily fight global warming since we would have direct and total control over the entire economy, no need to incentivise and hope corps go green when we can just do it instead. Another pro of many is that information would flow freely, without competition no one has an incentive to keep information private and progress can happen in a cooperative manner rather than being stunted, as evidences by how crucial openness is to the scientific community. Such a democratically planned economy would be fundamentally aligned with the interests of people unlike markets for which you have to hope that their profit motive aligns with the common good.