Okay, from what I've read this is the reason:
Litz wire works well because it helps reduce the skin effect. This effect is apparently more important to consider in high frequency (i.e. RF) applications.
The reason why stranded wire shouldn't be used is again due to the skin effect. The idea behind Litz wire is to increase the surface area of the conductor (by using multiple conductors) while reducing the skin effect (which is why each conductor must be insulated from each other).
This, however, brings up two questions:
1) I've seen many designs (including some posted here on AVS) which use Litz wire constructed with stranded wire. Are these designs incorrect, or am I still missing something?
2) All of the info I've found so far claims that Litz wire has most of its benefits in the higher frequency ranges (i.e. RF). If so, then why are there several designs for audio interconnects and power cords using Litz wire? It seems these designs would benefit very little from the Litz design.
site claims "Skin effect can be reduced by using stranded rather than solid wire."This
site claims "...you will find that it doesnâ€™t even become an issue until over 1GHz which is significantly higher then audio, component video and HDTV signals."This
article claims that "It does not matter if a Conductor is 12 Gauge solid Copper, or a Conductor of a 12 Gauge multi-stranded Cable...both will appear as 12-Gauge solid Copper round conductors."