For subsonic aircraft, would adopting a higher wing loading decrease drag?
Generally, you are right. Reducing wing area is reducing overall drag. Within limits.
Induced drag depends on speed and span loading. If the reduced wetted surface allows you to fly faster, reduced drag will be lower, leaving more of the power budget to overcome viscous drag. However, if wing span is reduced, induced drag will be higher at the same speed, so it is better to reduce chord than to reduce span. This can be witnessed by the recent development in airliners where the reduced fuel flow of engines has allowed to build smaller wings with higher aspect ratios. A similar but older example is the Davis wing which combined extreme root airfoil thickness and an aspect ratio of 11 to minimize overall drag and keep wing weight reasonable. Other aircraft designed for long range even sported an aspect ratio of 14.5!

If one wants to reduce induced drag, than one must fly at lower altitude.

Don't focus on induced drag reduction alone! Please remember that the lowest overall drag is at the polar point where induced and zero-lift drag are equal. Move away from this point and overall drag for lifting the same weight increases.
Turbine engines profit from colder air. Flying higher means higher true air speed for the same dynamic pressure. Therefore, wing area should be sufficient to allow operation close to the tropopause. Going higher than that does not improve things, but staying well below the tropopause means to forego an obvious advantage. Only airplanes designed for low level missions will have a wing loading well above the 600 kg/m² which is typical for airliners. That's the limit mentioned above.