But that aside, how would you handle public trading companies, where you can simply buy an influential part of a company?
It is not the same as owning or merging but having board influence can also be detrimental.
Depends. What are the arguments for a company holding shares in another?
If the purpose a company X has shares in Y and Z to diversify their income stream then perhaps non-voting stocks would be suitable.
If a company holds shares in another company because they are somewhat dependent on it being run and facilitated in a certain way, it makes sense that they'd want to have an influential share but if they are rich enough to acquire such a stake then they are probably a valuable enough customer that the company they depend on won't do much that upends the entire business relationship. Or is that naive of me?
If all big mergers are banned and if all megacorps are banned from acquisitions, then maybe also ban the idea that companies should have voting rights in other companies? Now, a wealthy enough CEO might sidestep that as a non-corporate entity, and may do so by some degrees of separation if they themselves are judicially blocked from such holdings so I don't have a ready-made fix for that.
You're falling for the "politician's syllogism": Something must be done, this is something, therefore this must be done. But it's called a syllogism because it's flawed logic. The worse the situation, the more important that we do something that actually helps, not just some random something.
This would probably be the way.
When a corporation is large enough to wield significant political influence, allowing them to buy up and coming disruptors makes it even easier for them to, as the article writes, make a mockery of democratic norms. And thus, by the same token argument, the acquisition of smaller entities should similarly be blocked.