Why complex landing gears are used instead of simple, reliable and light weight muscle wire or shape memory alloys?
Shape-memory alloys change their shape with temperature, with control usually achieved with electric heating in one direction, and back with convective heat transfer to the environment. There is one specific temperature where the change in shape occurs. There are two huge problems with this:


The operating temperature range for gear actuators is huge. It may easily be below -40°C on a cold arctic night, but on a hot tropical day the sun can easily heat the structure to upward of +60°C. That means the transformation temperature must be pretty high, but that means a lot of energy has to be put to heating it, especially if the ambient temperature happens to be low on the day.

Note that the actuators are not very energy efficient. A super-capacitor can give you high peak power if you need that, but will not help at all with the total energy. The work the actuator has to do is significant, so the efficiency matters.
Worse, a shape-memory alloy actuator requires constant power to remain at one end of the motion range and spontaneously returns to the other. However, gear must be stable in both end positions without requiring energy, so there would still have to be uplocks and separate actuator for extension or retraction (or maybe extension would be gravity-only, but then you have to ensure it gets reliably locked). Not really simple anymore.


I also don't think they actually scale to the required forces and displacements well. A 2 mm wire bends quite easily, 2 cm rod, not so much. The thicker will of course need more force to bend—which is OK—but it will also break much sooner, because the difference in strain is bigger.