Interceptors are not missiles. They do not have a warhead (in the typical sense) Or let me put it like this. This is the Kill vehicle of an SM-3.
This is the Kill vehicle of Groundbased Missile Defense
Thsis is a schematic for a SM-2 (and SM-6), which is an anti-aircraft / anti-ship missile that shares technology with the SM-3.
The SM-2/SM-6 can fly a ballistic trajectory and impacts it's target with a warhead that detonates and causes an explosion. An SM-6 in an anti-air role does not fly a ballistic trajectory but in a Land Attack or ship-attack role, it would. And it has a warhead capable of causing explosive damage.
The SM-3 and Groundbased Missile Defense fly NON-Ballistic trajectories and utilize a
non-explosive hit-to-kill vehicle. Think of the kill vehicle more like a small suicide satellite than a warhead. They destroy missiles through kinetic energy (their mass and speed), and not an explosive. If you could, somehow, launch an SM-3 at a land target, it would be like firing a satellite at something. It's an absurd proposition.
What is based in Europe is the SM-3.
These are not general purpose launch vehicles. They are specific things and a missile can't just carry any payload. I hope you can regonize how fundamentally different they are. You can't use a ULA Delta IV Heavy a nuclear weapon launch vehicle / ballistic missile, even though it is "rocket" just like the SM-3. I go back to my B-52 vs Blimp comparison. Flying and flying the same way / purpose are very different things.
Furthermore, treaties govern these specific things. The ABM Treaty governed ABM systems. The INF Treaty governs Intermediate Range Systems. Trying to shoehorn one into another is nonsense, and the fact of the matter is a tremendous amount of work goes into these treaties to make sure, specifically, they don't allow for that.
With NewSTART for example, the US worked very hard to make sure that under no interpertation of it does our forthcoming Prompt Global Strike weapons (which will be activated within the lifetime of the treaty) count as a nuclear warhead OR a "Launch Vehicle", subject to treaty limits. It was a big goal of the negotiations because the US is investing very heavily in PGS and will be doing more so in the years to come. That hasn't stopped Russia, however, from ALREADY trying to accuse PGS as being treaty breaking, even though they themselves agreed with the principle that it wasn't.
This is how Russia plays their stupid games, and the thing is, it really doesn't matter. SM-3s are going to keep popping up a cross Europe and PGS is still going to be built as needed.