You ascribed then (and ascribe now) a level of sentience to markets which just don't exist. A market cannot decide to go against demand or supply, no matter what the people which it comprises believe.
You are either misunderstanding me or human nature, i'm not certain which. You seem to be assuming that the market is neutral when that is very much not the case. The market is made up of humans, and those humans are in no way neutral. If the people who make up the upper levels of the market, for example, hated black people then the market would discriminate against black people. If enough people in the market believe the same thing then the market will reflect that belief. If enough people who control major companies create a culture where labor is undervalued, then it is undervalued in the market.
But the things you are proposing still don't make sense; the ruling class (capital) not wanting to pay more for labor does NOTHING to change the supply of labor, it changes the demand.
Why are you under the impression that you need to control both the supply and the demand of labor to control the price? If I and a small group of others control most of the jobs in a town and we decided that we would not pay more than X amount. Then it doesn't matter what workers want. They will either make the amount we decided, or their families go hungry. If the culture of the people making up the market is to under value labor so they can maximize profit, it doesn't matter what the supply is. They have nowhere else to go. There is nothing they can do if everyone (or the majority of companies) are all under valuing them. So by creating a culture where you pay as little as humanly possible to employees, while simultaneously undermining any sort of unionization, companies can get away with paying as little as they can.