Like most Americans sadly, we look to the short term goal not the long term one.
When Nixon went to China the ChiComms and Soviets were shooting at each other. Nixon GAINED NOTHING from allying with Red China - the Chinese were already hostile to the Soviets. His feat was not great diplomacy at all then.
What would have been great diplomacy would have been to ally with India. Soviets and Red Chinese were like oil and water - let them fight it out. Soviets would be allied with Muslim Pakistan? Doubtful it would have produced anyhting - oil and water again.
Well China did put pressure on the Soviets from the rear giving them two fronts to look at as opposed to just Europe. Also you forget India was still under the whole anti-Western Imperialism and saw the US as a bigger version of the British Colonialism they just left. They actively courted the Soviets for friendship as well