Should BBCI team be the only Indian team ?

The Board of Control for Cricket in India, or BCCI, is the apex governing body for cricket in India. The board was formed in 1929. It is a society, registered under the Tamil Nadu Societies Registration Act. The BCCI often uses government-owned stadiums across the country at a nominal annual rent. It is a private club consortium. Basically to become a member of a state-level association, you need to be introduced by another member and also pay an annual fee. The state-level clubs select their representatives (secretaries) who in turn select the BCCI officials. As for any private club, BCCI or the state-level associations are not required to make their balance sheets public. {Source from WIKIPEDIA}

The Board of Control for Cricket in India was established in December 1928 as the single national governing body for all cricket in India. It is headquartered in Mumbai. {Source BCCI web site http://bcci.tv}

Who gave the right to the BCCI to clam that they are the only team which can represent the country. BCCI is not a government organization and it is not entitled to show its revenues to the public. If it clams that it represents Indian, should the Indian people have a say in it's functions ?

Why cant any other board like ICL clam that they are the representatives for the country in the world stage?

Why can't the Indian government take over the BCCI and run it, why can't the BCCI be placed under Sports Authority of Indian which is under Sports Minister?