When dealing with missile systems, nothing works 100% of the time, nor do they hit a target every time it's fired, to think otherwise is pure fantasy. This isn't Quake or Unreal.
The first thing to remember is that the United States isn't the only country working on these systems. The Russian Federation has a ring in place and is expanding their advanced S-300 and S-400 deployments around cities, India is working on systems with tests scheduled for this year, the Japanese have access to all of the Patriot and Standard R&D and test data and are adopting them too, Israel is working on SRBM and MRBM interception missiles.
Even when dealing with nuclear weapons, no warhead hits the target directly or close enough to destroy it 100% of the time, this is why when dealing with force and counter force calculations, multiple warheads are targeted at a point.
Adding interceptor weapons, something the Russian Federation already has batteries of around Moscow and St Petersburg, to the US arsenal gives the US a chance to intercept a small decapitation strike, or to attrit it enough that it isn't guaranteed to be 100% effective.
For small nuclear arsenals like North Korea or a nuclear Iran, a battery of interceptors could be better than ~70% per interceptor, eliminating a small arsenal's threat value. For medium sized arsenals like France, Great Britain, Pakistan, India, Israel and China, interceptors would make them devote more of their force and counter force warheads into a strike.
The Russian Federation getting so upset by a handful of interceptors either means their current ICBM and SLBMs are very vulnerable to boost and post-boost interception or they only plan on using a handful of missiles in decapitation strikes, which is the only thing US ABMs could deal with in regards to the Russians.