"From static positions" is the point Stuart. To "break through" later in the conflict, enemy mechanised forces would have had to travel down single roads at the bottom of steep valleys. They would have been easily interdicted by AT weapons. artillery, mines, obstacles and demolitions. Even to attempt that they would have had to time their attack for bad weather because they would be creating a dream target for air interdiction, assuming they made it out of their assembly areas. There is a reason the last two years of the conflict were primarily an infantry affair.
Rather earlier than that. We lost at least 2 Centurions in the Imjin battle to Chinese soldiers with explosive sticks.
I don't believe that was why the war was static though. I think it was more an unwillingness to face the casualties it would take to move the front line, armour led or not.
Yes, we could have advanced, but Truman in particular was not willing to pay the price of advancing through mostly incredibly defensible terrain or of the conflict escalating into a general war against China and Russia. I'm sure we could have advanced, at great expense, given enough resources, but we had air supremacy (superiority nearer the border) and the ability to strike from the air at will, weather permitting*. I can't see how the communists could have made significant inroads. There were occasional exceptions to this. If you google the 72nd Tank Battalion and Mundung-ni Valley, you will come up with one.
*Ground controlled radar bombing may have been possible.