Aegis GMD has zero effectiveness against a missile field filled with SS-19s, or mobile SS-27s, or anything else that poses an existential threat to the United States. Russia knows this. "Destabilizing" would be an order of magnitude increase in the GMD interceptors at Greely and Vandenberg and the proliferation of battle management radars, and we aren't doing that.
And if you weren't paying attention, there's no "restart" of the arms race. While the US was involved in the -stans, Russia was moving forward with a variety of delivery systems. The race never stopped.