The Soviets had missiles and the R-7 ICBM [operational on 09 February 1959] before we did and CONELRAD was specifically designed for the bomber threat. After the bomber threat was found to be non-existent [see NATO code name - BOUNDER], CONELRAD was terminated.
Missiles use gyroscopic and inertial navigation for guidance, not HF/DF, TACAN, GPS/GLONASS, or other signals that can be spoofed or shut down. All ICBMs and SLBMs are independent entities when launched and cannot be recalled. They can be intercepted by ABM systems, subject to fratricide at target, fizzle, or subject to internal fault/failure.
The whole plan for SCATANA was to clear US airspace for the use of ICBMs and US bombers. ICBMs are launched initially, but not all at once. Bombers can take a while to launch towards their targets, especially if they had been deployed to secondary airfields and civilian airports as pre-conflict tensions mounted. A secondary use was for ADC/TAC/ANG interception of any aircraft flying over, towards, or near the US as hostiles.