Because it's close to impossible. To compete with Google in its primary business of search/advertising you must

1) be much better at it, or no one will switch

2) have enough money for the equipment to handle the crazy amounts of traffic

3) have enough money for the engineers to build all that

You have to realize how huge and fast google already is. You make a post/comment on Reddit, it's in the search results within minutes.

What features would it take for you to switch from Google? Even if some giant like Apple would spend billions and launch a search engine, how many non-apple users would use it? My guess is - not that many. Google has become a verb. "Just google it".

As far as I can see, you can beat google in some niches, like DuckDuckGo that rides on the wave of privacy.

Because search engines are a winner takes all market. There is no reason for anyone to use the second best search engine and so there will be a tendency for everyone to migrate to the best one. Plus they are now the incumbent so you would really need a new search engine that is significantly better for people to notice and start switching.

Google is also vastly better at monetizing search than its competitors. Revenue per search at Bing or Yahoo is just a fraction of what Google makes. That is what makes their advantage permanent.

I always wondered if Bing gave away $1M a day in a sweepstakes to it's users if people would switch.

You can be Google mini competitor ;) Join to bubblehunt.com - this is search engine for your information

In what - search? Maps? Mobile? You could be a bit more specific.