The problem are money, IRC the sistem were not cheap and to develop this type of system plus the nuclear deterrent sufficient to cause significant damage to the enemy can bankrupt both nations and not forget the conventional force, as the presence of a efficent ABM defense enfatize the conventional aspect of a conflict between Nato and Warsaw Pact so you must add even that expense. And remember that for intercept the ICBM you use nuclear warhead so be prepared to some enviromental damage and higher rate of cancer at least in case of launch.
Also, it costs more to intercept an incoming warhead than it does to launch it. Several times more, especially with the technology available in the 60s and 70s, because you have to target each incoming warhead with multiple missiles to get a decent kill probability. So it's significantly cheaper to build more missiles to overwhelm an enemy defense system than it is to build the ABMs to shoot them down. The economics may change with beam-based missile defense, but that didn't exist in the Cold War.
There are also serious C3I and detection issues, especially if you want it to work against SLBMs as well. You have very little time to decide whether or not to launch the nuclear-tipped interceptor before it's too late. And the original Safeguard/Sentinel concept had problems with blinding its own RADARs when the Sprint ABMs detonated. And the sensor systems are vulnerable to attack; knock them out and the system's dead. And the decoy issue. And so on.
A more limited missile defense intended to defend against China and other third parties, or against accidental attacks, might be possible. This could also serve other roles as well - for example, it would complicate enemy targeting. You don't know what I'll choose to defend, so you have to allocate extra warheads to take out "must destroy" targets, like missile silos. But it's not going to block a full strategic attack by a peer competitor.