Yes, of course what you quote is true -- more resources favors large entities and corporations. Similarly for example, the rich versus poor when appearing before the legal system. That is a deep problem of democracy + capitalism.

But if the desire is to reduce the influence of money in politics and the weight of corporations in our lives, that is something for Congress and our laws to be modified to do. Similarly to decide to tax, redistribute, or equalize the playing field between rich or poor. You would not have a court decide what tax policy to enact, or what the thresholds of welfare or social security brackets are. Courts are to resolve concrete disputes between individual parties using principles derived from the law, not promulgate new laws.

Courts have to treat people and entities coming before them in cases as equal parties, based on their arguments and evidence. If the side of corporations have more resources to pursue cases, hire lawyers, and fabricate evidence, etc. than individuals, then that's something for Congress and laws to fix. Courts are not here to somehow say that when there's a dispute, individual people's arguments take precedence over a corporation's when the law is clear about enumerated rights or regulations. Or to say a general policy principle like "people's rights trump corporations' rights". That is not a justiciable statement.

The relative rights of people versus corporations is where laws should lay out those definitions, in the places and applications where the theoretical becomes the real. Not for courts to create novel rights that are not subject to the democratic process and checks/balances on such important questions. Or if they're not specified in the Constitution.