I fail to see how this is any better than existing first strike weapons.
Anti-anti-ballistic-missile technology doesn't mean much when anti-ballistic missiles barely work, and all your adversaries have lots of rockets each with lots of reentry vehicles.
Maybe destabilizing means we, the US now have less time to make a decision on a first strike by Russia and the potential for an incorrect analysis leads to a retaliatory strike before we lose the ability to do so.
Dissuasion must be credible and that requires credible delivery systems (missiles).
Thus, if for example the US develop anti-missile systems that are able to shoot down Russian missiles then Russia no longer has a credible dissuasive arsenal. Consequently Russia must develop new missiles that evade anti-missile systems. This does not mean that they are designed for first strikes, it just tells the US "don't hit us because we can really still hit you back".
It's the age old race between offensive and defensive systems.
Anti-anti-ballistic-missile technology doesn't mean much when anti-ballistic missiles barely work, and all your adversaries have lots of rockets each with lots of reentry vehicles.