Great, I want people who work hard and are productive to have more influence. I also want to prevent unethical ways of enrichment.

Personally, I do not, because they make decisions like "I should have to pay less taxes so I can have even more money and I do not particularly care that the trains are barely running and constantly late, since I never take them anyway."

Is that fact true in all times and places? Can the amount of power and influence per dollar be reduced somehow?

In a sense you can think of money as a way of measuring influence, since it is an abstract way you can compel people to labor on your behalf or give you resources.