The decision to develop and deploy W88 warheads on Trident II, didn’t happen in a vacuum.

Soviet and American nuclear war doctrine reduced down to two scenarios, Countervalue, (City Killing) and Counterforce. (What you refer to as first strike)

With the deployment of the R-36M, and its 10, 750kt MIRV’s in 1976, the Soviets moved to an unmistakable Counterforce posture.
They reinforced that notion in 1978 by deploying the destabilizing RSD-10, also, clearly a Counterforce weapon.

It took us 10 years to finally counter the R-36, when the (totally snake bit) MX began deployment in 1986. (Likewise, Pershing II finally countered the RSD-10 in 1983)

So US Counterforce policy wasn’t arrived at capriciously, or unilaterally. It was literally, self defense.

At the time, SLBM’s were far from accurate enough for the Counterforce role, but fortunately, by the time we negotiated the MX away, under START II, the Trident II D5’s were available.