Why did was there no direct conflict between the US and the USSR in the Cold War?

By 1950, both the USSR and the USA had successfully developed and tested nuclear weapons. For both countries, spending on research and development for more advanced nuclear weapons was a top priority, as a way to prove their global dominance and ideological superiority.
However, nuclear weapons were never used by either country against the other because of mutually assured destruction (MAD). This means that both countries were aware that, if they were to use their nuclear weapons, the other country would retaliate and completely destroy the other.
This meant that the Cold War did not involve direct conflict between the USA and the USSR and instead focussed on propaganda and proxy wars (where both the USA and the USSR would involve themselves in smaller regional conflicts, supporting whichever side they ideologically agreed with.