Why are the stabilised approach criteria different for an instrument approach and a visual approach?
All instrument approaches are not alike. The Flight Safety Foundation Approach-and-Landing Accident Reduction Tool Kit, Section 5.1 — Approach Hazards Overview points out


Fifty-three percent of the accidents and incidents occurred during nonprecision instrument approaches or visual approaches (42 percent of the visual approaches were conducted where an instrument landing system [ILS] approach was available); …
Fifty-nine percent of the accidents and incidents occurred in instrument meteorological conditions (IMC); …


For a precision ILS approach, the ALAR recommends additional criteria in that the approach must be flown within one dot of the glideslope and localizer.
The thousand-foot gate is clearly driven by the worst case of a circling approach where the aircraft is not aligned with the runway, must transition off instruments back to visual flying, make the appropriate maneuvers, and land safely. Those all take time, so we should expect the recommendation to be at least as high as the visual approach.
In Section 7.1 — Stabilized Approach, we read

In addition, a stabilized approach provides

More time and attention for monitoring ATC communications, weather conditions and system operation;
More time for monitoring and backup by the PNF;
Defined flight-parameter-deviation limits and minimum stabilization heights to support the decision to land or to go around; and
Landing performance consistent with published performance.