I'm not the other poster, but there's at least 3 reasons.

1. Competition doesn't just happen for consumer goods, it happens for every single commodity traded on the market. Labor is a commodity. Because of the immense supply of labor, and the capitalist class' deliberate decision to maintain an unemployed section of the population which deflates wages by adding more desperate people willing to work for less. Generally, you can think of a market as a battle between 2 armies who also have internal battles. If the attacking army is better at organizing itself and doesn't get mired in the internal conflict, while the defending army is divided and has constant mutinies, the attacking army is bound to have a better chance in the battle. The capitalist class is smaller and has a much easier time coordinating, most workers don't have large enough unions to contend with that.

2. Competition only goes on for so long, and eventually the whole point of a competition is that someone wins. If you have several companies competing to set the price of a commodity in a market, odds are one of them has enough capital to starve out the other ones. That happens in the real world all the time. What's worse, the more times you capture parts of the market, the easier it is to capture more. That's one of the fundamental tendencies in capitalism, the centralization of capital under fewer and fewer hands. Of course, once this process has run its course the result is monopoly, but even if the companies step short of monopolizing the market entirely to avoid anti trust regulations they are still likely to draw agreements between themselves to keep prices at a certain level to maintain profits. Recall the armies analogy above.

3. Even if nobody won in a competition and there was some permanent state of lowering the price of goods, while this is "good" for consumers, it's still bad for the workers producing the goods, which most consumers are. Capitalists have no problem investing more fixed costs in the process of production if it leads to larger profits in the short term, but the issue comes down to the way profit is made in the first place. In a capitalist system, a cycle of production takes place when a capitalist exchanges money for commodities, pays a wage to workers who improve the commodities through their labor, then sells the commodities for more money than they spent during the cycle. The difference in the selling price and the fixed cost (capital) plus the variable cost (wages) is profit. Since the fixed cost is paid for at the same rate everywhere, i.e. no one should be buying the same commodities for significantly different prices at least locally, the only place where the difference could come from is the wages being smaller than the value added to the commodities through labor. Therefore, profit comes as a result of using labor that the capitalist bought at a discount. That discount we call exploitation. Now consider what happens if more capital is invested: the fixed costs grow in relation to the variable costs, but profit only grows if more labor is exploited. That means that the only way to keep commodities cheaper and cheaper still, while generating more profit relative to investment, is to ramp up exploitation. Practically we see this in reality in the way the production of some goods take place once competition runs its course; factories close down and capital moves abroad to where there are fewer regulations, sweatshops replace the factories and production can keep taking place because exploitation was increased.