Why US did not directly attack Beijing since they had maritime dominance ?

Peter Gore Seer,

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The short answer is that the UN forces, which were commanded by US officials, were involved simply to liberate South Korea. The main objective was to drive North Korean forces out of South Korean territory - that was it. SOME US officials pushed for widening the scope of the conflict, and suggestions ranged from small scale attacks on Chinese industrial targets, bases, and cities to hitting the Chinese with atomic weapons. In the end, it was decided that the US led UN forces would concentrate on pushing the North Koreans and their Chinese allies back without directly hitting China proper. That was partly because the Chinese had covered their arses by designating the Chinese troops involved in the fighting as "volunteer forces", thereby claiming that they were Chinese civilians who were compelled to fight for the North and were not being trained, provisioned, armed, and funded by Red China itself, which everybody knew was ridiculous, but it made it a lot harder to strike China directly because international opinion was open to interpretation when it came to the extent of the Chinese government's actual involvement. It would have also complicated matters with the USSR who too claimed to be passively observing the fighting, though several Soviet airmen were shot down over the course of the war and were repatriated. Essentially, the US led UN forces were confident that they could achieve their aim of liberating South Korea without switching the focus to hit Red China, and considering that they were toeing a fine line between fighting a proxy war with the communists and fighting an open war with both Red China and the USSR, they decided not to escalate things. 

In the end it would have been better had the US led UN forces insisted on reacquiring all of the DPRK, but the doves in Washington weren't willing to commit to that goal and to see it through. That's why the armistice was signed, leaving the border virtually unchanged, and the situation has continued on as it has been since 1953 with some flare ups over the years, but has never again progressed to outright war.