If NATO considers Russia to be one of its biggest safety threats, wouldn't accepting it into the organization remove the threat without unnecessary conflicts and casualties?
Accepting it into the organization wouldn't eliminate it as a security threat as states within NATO do retain their sovereignty and control over their military. Joining NATO would have allowed Soviets access to sensitive intelligence, access to technology and training that would have made it a larger threat. It could also have used it's membership to prevent action (similar to what it does on the UN Security Council). Additionally, allowing the Soviets to join would have defeated the overall purpose of the organization which was to reassure European Allies about the US commitment to their defense.
The most prominent case of the US offering to aid the Soviets was when Truman offered to include the Soviets in the Marshall Plan. This was an offer that the State Department fiercely debated, since they were concerned that if the Soviets accepted they would obstruct the process, but they also didn't want to give Moscow an easy propaganda victory. As a result, they extended the offer of aid with the expectation that the Soviets would reject it due to the strings attached. The Soviets blanched at the economic reforms required to take part and refused to accept and also ordered their eastern European satellites to decline.