At that point, innovation slows and prices can rise because there is no pressure.
In a completely free market, this is when a third producer of widgets will enter the market and compete with the monopolistic widget seller. The ability for anyone to enter a new market and compete with the existing players in that market is one of the keys to having a properly functioning capitalistic economy, yet this freedom is often overlooked by many. In your example, consider what would happen if the two original widget makers were evenly matched. After a while, they might both become complacent and the price of a widget might start to rise. As soon as an outside entity sees the widget market and decides that they can produce a better or cheaper widget, they will enter the market regardless of how many producers of widgets exist already.
The real problem with capitalism as currently implemented in the United States (and many other places) is that some markets have significant barriers to entry that new competitors must pass. The market for cell phones and mobile internet is a great example of these types of barriers. In order to enter the market, each competitor must have the use of some chunk of electromagnetic spectrum for their devices to use. Suitable spectrum is limited by simple physics so the number of competitors is clearly limited. Also the government has allocated some spectrum for other uses, so the available spectrum is even more limited. Without the ability for new competitors to freely enter the market, a natural oligopoly forms based on whoever has control of the spectrum, and competition is limited.
Note that the existing competitors in the cell phone market don't necessarily even need to collude to drive prices up. They can each independently examine the market and determine that since the market has become controlled by a limited number of entities, each competitor's profits will be maximized by keeping prices high. It might be true that in the long term, the most efficient competitor will do better by lowering prices to capture the entire market, but that will take years or decades to accomplish. And in the meantime, their profits could have been higher by keeping prices higher. We've all seen the obsession with next quarter's results, so it is no surprise which path is taken.
Wired internet services have the same problem, but with slightly different barriers. Many communities have exclusive franchise agreements limiting competition. But even without those governmental limits, future competitors face increasing resistance from residents because many people in a community do not enjoy having roads torn up to put in parallel infrastructure. Another problem is that geographically large competitors can artificially lower prices in areas where new competition happens to pop up. They may even take a loss in these areas for a short time until the new competitor is driven out of business. The large competitor is able to do this because they have captive areas where the prices remain high and can use the profits from these areas to subsidize the losses in the competitive areas.
These types of problems don't happen in markets without significant barriers to entry. Take the production of pencils. Anyone can start a company producing pencils if they wish. You can even make one at a time in your basement if you wish. Because of this freedom, pencil prices are driven close to the cost of production by existing competition, along with the threat of more competition if the existing competitors become inefficient.
In summary, I think the problem to which you refer is not one of capitalism itself, but of the current implementation. "Unbridled capitalism" does work in free markets, but not in markets with significant barriers to entry.