I am not a civil engineer by any means and am happy to be corrected, but a frost skirt is not a strip foundation. The former is meant to keep water away, the latter to transfer loads. They look similar in construction because concrete is poured into a trench, but they have nothing else in common.
Of course, you can build on strip foundations (and lay them at frost-free depth), but then the slab is dimensioned differently and no longer serves as the (sole) load-bearing element, otherwise it would unnecessarily cost more.
If the slab itself is used for load-bearing, you do not need a strip foundation, but you must somehow prevent the slab from being lifted by freezing water. This can be achieved with a surrounding, waterproof concrete wall, i.e., a frost skirt.
But just as well by replacing the subsoil with non-frost-susceptible material (e.g., foam glass gravel or the like).
The insulation of the (strip) foundation, or the edge of the slab, in turn, is intended to prevent thermal bridges at these points, but it certainly will not keep frost away. Strictly speaking, insulating these areas in this context is even counterproductive because it withholds the heat of the house from the soil there.