There are several problems with the credibility of this kind of assurance.Why would it destabilize anything whatsoever? It's not like MAD suddenly went away. Nobody in their right mind thinks the kind of defenses the US is working on would stop a full scale attack.
1) There is a historical precedent (SDI) of the US working full steam toward exactly such a full-scale capability.
2) Recently, individual US policy makers have started calling for efforts toward this goal to be renewed - so what do you know that they don't?
3) Unlike last time round, today there is no treaty in force that prohibits such a development, meaning the situation could potentially deteriorate much faster.
MAD has shown itself to be a rather frightening but encouragingly stable and resilient concept. Most of the crises it did endure were precipitated by one side trying to "beat the system" and gain an asymmetrical advantage over the other. In an environment where both parties were satisfied that they could still deliver a debilitating retaliation even in the worst imaginable scenario, MAD has even demonstrated potential for mutual threat and cost reduction by diplomacy and arms control.
As a result warhead numbers have gone *down* over the past decades, and significantly so - by contrast, BMD carries the very real risk that warhead numbers soar through the roof in order to accommodate the potential losses. Or that novel and risky delivery methods will be implemented to outflank the defences, inflicting huge costs on both sides. They would invalidate the investments in BMD on the one hand, impose expensive development programmes on the other side and potentially change the dynamics of the whole stand-off in destabilizing ways. For example, the characteristics of the new delivery modes might aggravate the risk of misunderstandings or accidents or incentivize early escalation.