Mutually assured destruction has never required all of the warheads make it to your enemy... or even that most of them do. In fact it is the exact opposite. Military planners have assumed since the late 40's and early 50's that most warheads would not arrive, but MAD still operates even in such a situation.
The name for this phenomena was originally, "the bomber will always get through," and then later, "the missile will always get through." Shortly after nuclear weapons were developed, the next question was how to defend against nuclear weapons. The short answer is that you cannot... or rather, you cannot effectively defend against a nuclear strike to the point where launching your own strike seems feasible. The basic reality is that nuclear weapons are so incredibly destructive that even a single bomb serves as a credible deterrent.
Suppose you want to launch a first-strike... is it worth it? The thought process goes like this:
- Suppose you can destroy half of your opponent's weapons in a first strike
- Then half of the remaining fail to launch
- Then half of the remaining are shot down by missile defense
- Then half of the remaining fail to land on-target
- Then half of the remaining fail to function
- The remainder detonate successfully.
At the bottom of the list, only one out of every 32 adversary warheads successfully detonates on target, or only a 3% success rate. If your opponent has 100 nuclear weapons, then that means three bombs succeed and make it through. A single nuclear bomb, especially by late 50's and into the 60's and certainly today, is more than capable of functionally destroying a city.
So here's the political calculus. Suppose you're President Kennedy- you can launch a first strike and obliterate the entire Soviet Union, but three of their weapons make it through and land on three American cities. Is that an acceptable exchange? Suppose you get to destroy the entire USSR, but Washington DC, New York, and Los Angeles are turned into smoking craters- three of the most populous and influential cities in the nation and the world. Are the American people going to stand up with you and applaud you for a job well done? Are you sure about that? What about all the people who had friends or relatives living in those cities? What about all the businesses that had clients in those cities? What about all the people who depended on those cities for services? Then add into that all of the anti-war folks, peaceniks, environmentalists, and anyone else who doesn't like the idea of lighting off thousands of nuclear weapons. When you have to run for election again, are any of those people going to have second thoughts about you in the voting booth?
Maybe some people would gladly trade grandma and their livelihood to see the USSR reduced to ruin, but most people won't. Or at least as a politician, you can't be sure either way. Any nuclear exchange could easily become political suicide, even if your opponent's weapons only have a 3% success rate.
And this is the reality of nuclear weapon defense. Nuclear defense only works if you can guarantee your system works 100% of the time, or maybe 99.9% of the time. It does not work if it only works 97% of the time, or 95% of the time, or 90% of the time, because your opponent has hundreds or thousands of warheads, and that could be three, six, a dozen or more cities turned into smoking craters.
In reality, under practical scenarios, nuclear missile defense has nowhere near a 50% success rate. If for no other reason than a lack of available interceptors. In the USA, the mid-course interception system, or GBMD (Ground-Based Midcourse Defense), is the only anti-ballistic-missile technology capable of defeating the large strategic ICBMs that would carry nuclear warheads from Russia or China to the USA. There are only 44 GBMD interceptors available. Even if every single interceptor was successful (which is not likely), the major nuclear threats to the USA have hundreds of warheads and launch vehicles.
If any of the assumptions in the bullet-point list above are not true, then your adversary is not just landing three weapons on your country, they are landing dozens or hundreds. If you only have 44 interceptors and they launch 300 separate missiles, then hundreds of missiles are getting through. If you thought only half of your opponent's missiles would function, but instead 95% of them function, then hundreds of missiles are getting through.
The other US anti-ballistic-missile systems such as THAAD or Aegis are not designed to be used against large intercontinental ballistic missiles (they are designed to intercept short- and medium-range missiles), and while US military forces are prepared to employ these systems in such a scenario, that's really a last-ditch effort and it is not expected to be effective.