That is naive, fails Econ 101. If the market is not very elastic, you get very little extra volume if you lower prices, and you get LESS profit.
What happens in a market that is elastic because overhead costs of doing business fall opening the door to competitors undercutting prices to their market advantage? Lower costs make room for higher profits at lower prices.
Sometimes, the market is highly elastic and cutting prices hugely expands the total market by bringing in new large classes of customer, and everyone benefits (e.g., PCs during the 80's and 90's). Eventually, though, the market is bounded and you return to the scenario in the first para, like PCs now.