As I recall, the WGS84 meridian is registered to the center of the Earth from space, whereas the classic Greenwich meridian is essentially registered to the loc

As I recall, the WGS84 meridian is registered to the center of the Earth from space, whereas the classic Greenwich meridian is essentially registered to the local direction of gravity at a point on the surface. If the local direction of gravity passed through the center of the Earth then the meridians would be the same. However, the Earth's gravity is non-uniform which causes the local direction to be slightly deflected away from a path that would pass through the center of the Earth as is the case in Greenwich. The WGS84 prime meridian is parallel to the Greenwich meridian but slightly shifted so that it actually passes through the center of the Earth. Because WGS84 meridian is not registered to a point on the surface (for good reason), it was always going to drift away from the Greenwich meridian over time regardless.