Arms control treaties are negotiated in the current context, in country's best interests.
Even a desire to build more ICBMs is harmful, as it makes a country less likely to voluntarily agree to ICBM limits in the future. But absolutely agree that ICBM and missile defense are intertwined, so only make sense to negotiate strategic arms control covering both.
I would say that it does follow that "sufficient" interceptors, relative to a counterparty's ICBMs, leads to a "successful" first strike.
Where "success" in this calculus means acceptable losses.
The lynchpin of MAD is that no one is insane enough to argue that the incineration of a major city is acceptable for a first strike.
Without ballistic missile defense, that destruction is effectively guaranteed, as long as the counterparty has available ICBMs and is able to launch them.
With ballistic missile defense, there's a chance that destruction could be averted. And that chance drastically balloons the risk of a first strike being launched.
To put it another way: you're the president, and you're at a meeting of the Joint Chiefs. Open conflict with Russia has broken out in Eastern Europe. Massive amounts of Russian reinforcements are transporting towards NATO lines.
No BMD: if we escalate to nuclear, and the Russians retaliate (as stated by their nuclear posture), American cities have a 100% chance of being vaporized.
BMD: ... American cities have a 75% chance of being vaporized.
That's a terrifyingly different decision, because it opens the possibility that someone decides to take a risk. Because there's a chance things will work out favorably.