Solid metal conducts electricity because metal atoms have the characteristic electrons in their outer shells that are easily moved away from one atom to the next to produce a current.
Metal in a solid state is the most common electrical conductor we use. All of our transmission, building, appliance and computer wiring is solid metal drawn into wire.
Solid metal is used to reliably carry electricity because it is strong, durable and cost effective.
Wire is made mostly of copper, which is one of the better conductors of electricity that is abundant and affordable. Ideally we would prefer to use silver wiring, a better conductor; but the cost of this less available metal would be prohibitive.
Copper is extensively used in wiring buildings as it is a reliable and safe conductor hidden inside walls.
Transmission lines require a material with a higher tensile strength to support its hanging weight and wind forces, so in this case, ACSR (aluminum conductor steel reinforced) cable is used.
The base metals are less expensive, but their reduced ability to conduct results in significant line losses. That is why the voltage is so high in transmission lines.