Why would companies becoming more centralized make "putting your money where your mouth is" less effective?

Because it can become hard to pick a different brand since there really aren't any choices at all: it's a monopoly.

You seem to be addressing a related but separate matter, namely boycotting products to influence companies. The topic in hand is companies pretending to be large numbers of anonymous people. This is what would be prevented if submissions to public consultations were tied to real-world identities.

Because they will start to have a monopoly and consumer choice will be so little, that you can’t avoid them.

I think this is a miscommunication. You interpret nine_k's phrase "putting your money where your mouth is" as meaning "buying only from companies you support", but I think nine_k actually meant "having public comments require payment".