"Wouldn't a business want to strive to be the best?"
No. A business wants to strive to be profitable. Market share means nothing if you can't achieve a profit. Many companies have strived to gain market share and have gone down the drain because they couldn't operate profitably.
The primary goal of any business is to increase the bottom line.
The only exception to all of this are start-ups which are seeking to be bought by a larger enterprise (such as YouTube or many other internet start-ups).
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