Copper wire is typically braided. This is done because braided wire is more flexible than solid wire of the same diameter. Being more flexible means it is easier to pull through conduit or roll off a spool. Let's not forget the appliance and extension cords.

Braiding triangular wires would result in uneveness in diameter when braided. It also occurs to me that the edges of a triangular wire would be more likely to cut the insulation.

Round wires are also uniform at the ends where you would be attaching the outlets and fixtures. With a shape other than round you would have to twist the wire to a proper alignment to attach it to anything.

Most house wiring is solid wire, copper or aluminum, although aluminum is not used any more due to fire hazards. Fastening copper wire to most household fixtures is not likely to be a problem, copper is soft and distorts easily. Besides, a round cross section only provides contact tangent to the side of the wire whereas a triangular section may provide a flat side for contact.

A triangular cross section is only a suggestion. A convoluted or star shaped cross section could also be employed. Transformers and motors both use wire and plates that aren't round to reduce size, weight, and cost. Printed circuit boards are probably the most efficient sort of wire circuit. Perhaps printed circuit boards could replace house wiring. Any other problems?

Better than a triangle would be a flat ribbon. It is easier to braid, insulate, and terminate, although it would take a major redo of electrical fittings to accommodate it, retraining of electricians to handle it, and of course all sorts of testing, approval, and code changes.

IMO it would be much better to make a profound change in our energy usage so as not to need so much copper (flat or round) or other metals in our electrical systems we'd otherwise need.

See the heading? I'm only talking about solid copper wire, like the kind used to wire homes and buildings. Any shape besides round would be an improvement.

The quantity of energy use is another topic.

Yes, but regardless, a viable way to reduce the amount of copper needed is by reducing the power the load supplied by said copper lines. And yes, one could combine load efficiency with flat or whatever copper conductors, if the physics are any good.

I suppose you drive a car with a 40hp motor because that is all you need to go 70mph. That would be like wiring a house with a 100 amp panel. Its not realistic to limit power consumption without considering future demands and allowing for the generation of new energy from some more efficient source.

I am not well educated on electricity but did have a basic class in high school a while ago. So feel free to flame me if I'm off base with this question.

Electrical resistance causes heat to build up in the wire. In a round wire that heat is evenly distributed. If the wire were another shape would there be a risk of parts of the wire being hotter than the rest, which might lead to melting insulation and fires?

You are right about the wire heating up. That is what fuses are for. Printed circuits have the ultimate in sharp edges, but they work great for their intended use. All I meant to suggest was that round wire is the least efficient use of material. Sharp edges can be circumvented by using curved shapes. A convoluted star shape might be ideal.

Not correct. Electricity is not just conducted along the surface but the whole cross section.

copper wire could be hollow to allow for coolant to pass(gas or liquid)no matter the gage!

The electricity conducted by a wire is conveyed along its surface.

You're talking about the skin effect, but at 60Hz it does not come in to play in the conductors commonly used in house wiring. For DC wiring it does not come in to play at all. Look up skin effect in wikipedia for a good overview.