No company actually wants it.
I disagree. If that was the case, then the Big Three would have let each other fall decades ago. However, they helped each other recover from past recessions for the sake of (in this case, American-based) competition.
Also, the fall of Circuit City left Best Buy flooded with customers. While you might think this is a good thing, they actually had to turn away Geek Squad customers for a time because their workload was too great for them to handle (even Geek Squad City was running out of room for the demand).
Microsoft is another example of a monopoly ultimately hurting a company. They're finally starting to pay the price of not improving their software (IE being a prime example) without competition. As a result, they now have to overcome the reputation that their software isn't secure and is behind the times (regardless of whether said reputation is earned or applicable to new software, that perception is still there).
And yes, while companies do strive to "take out the competition," when it comes down to it, the competition helps them thrive, and most good business owners know this.
After an instrument has been assembled, extra components will be found on the bench.