I don't see how the Golden Dome could change the strategic equation for many reasons:
1) Achieving the ability to have hundreds or thousands of heavy space-based interceptors that can accurately track and intercept ballistic missiles from the boost phase would require astronomical amounts of money, money that the US is already struggling to find for its day to day military needs (R&D, procurement, maintenance, etc.).
2) The required satelites would be huge, easy to track, jam or destroy. I mean what's stopping Russia from frying them with an improved peresvet system, even during peacetime? No nation would want to have a weapon system taking a stroll above their land. It's equivalent to saying that a strategic bomber has the right to fly above you at any time if its altitude is more than 100 km. It makes no sense to me.
3) There are already delivery systems that negate whatever advantages the golden dome might theoretically provide, such as the nuclear powered cruise missile or the nuclear powered deep-sea torpedo. All Russia or China have to do is continue to improve them and manufacture them in far greater numbers. At that point economy of scale will take over and make them cheaper. We also shouldn't forget about strategic bombers. They were deemed inferior to ballistic missiles in the past, but they're still pretty good, especially if they were made to be stealthy or hypersonic or both.
4) Strategic balance can be restored by simply building and deploying an equivalent system. Something that China can easily do and Russia would be able to do if they designate it as a priority. But that would also mean that warfare would have to fully transition to the space domain, with counter-interceptors and counter-counter-interceptors. Eventually culminating in space fighter planes. But that's a can of worm I'm not sure the US would be willing, or could afford, to open.
