Why does the government believe it has the right to intervene in markets to promote competition? Is this consistent with the idea of laissez faire and free markets?

The government believes it has the right to intervene because a lack of regulation or intervention causes monopolies, which cause market domination, the instant crushing of competition, unfair price hikes to consumers, etc. The government believes it has a duty to protect the rights and interests of citizens, and sometimes monopolies can go against the rights and freedoms of citizens, if they get too extreme.

Government intervention in the economy is not consistent with laissez-faire, because laissez-faire dictates that there should be NO government interference in the economy at all. It is semi-consistent with free-markets, depending on who you ask. For example, a libertarian or hardcore capitalist might tell you that a semi-regulated free market isn't a "truly free market." But that's more of a fringe answer. Most people believe that markets can still be considered free markets, even with a little bit of government intervention.