Am I thinking about this correctly regarding 12V, 24V and 120V LED lighting?
Safety. Low voltage won't kill someone that comes in contact with the wiring.
Insulation. Related to (1), the higher voltage strips will require better insulation.
Cut-to-length. Figure 1 and 2 show the typical setup for a 12 V strip. They can be cut to length at any of the scissors points without any dark LEDs. The higher the strip voltage the more LEDs per section and the longer the sections. This affects their usefulness in many applicatons.




Figure 1. Typical flexible striplight. Images: Flexible LED strip light



Figure 2. Schematic diagram for Figure 1.


The mains powered strips are likely to have forty or so LEDs in series. If any one goes open circuit the whole strip will fail.