The original 1D was released in mid 2001 before 36x24mm sensors were viable for a production camera - so it was made with the largest sensor available at the time - a 1.3x crop sensor. The mount was EF, and EF-S (which only has an imaging circle big enough for a 1.6x crop sensor) hadn't even been introduced back then (that happened in 2003).
The first ever production FF DSLR was the Contax N of spring 2002. The 1Ds was the second FF DSLR, launched in September 2002, allowing of EF lenses with the conventional film AoV.
The 1D successors carried on with its crop sensor, allowing for fast sensor readout and consequently frame rates, and the 1Ds range carried on with full frame sensors, and slower readout/shooting.
The 1D X is an amalgamation of these lines.