The choice of solid vs stranded wire is based on the physical properties of copper. If you bend a copper rod (like a wire) through a bend with a radius of 3 or 4 times the diameter of the rod once, the stress causes the formation of crystaline structures at the site of the bend. If you bend it that way a dozen times, the wire will fracture along the crystaline boundaries. This is work-hardening and fatigue.
However, if you bend a copper wire through a bend with a radius of 1000 times the diameter of the wire, there is very little stress on the wire, and it takes tens or hundreds of thousands of bending actions to form crystals.
So, in your house, where most bends aren't sharp and the wire doesn't have to flex from day to day, with the exception of where the wire wraps around a screw for a connection, there's no place where the wire can work harden and break. And, wire with one strand is cheaper than wire with many.
For applications where the wire has to bend, a bundle of thin strands allows the wire to flex through some fairly steep angles without work hardening. The flex radius is many times the diameter of the individual wires even though it might only be 5 to 10 times the diameter of the finished bundle.
So, stranded wire is used where any flexing is required, and solid is used where flexing is not an issue.
As for surface effects in AC, I worked it out once and it's immeasurably small at 60Hz. It's simply not a factor. What is a factor though is that, where practical, you make a buss structure that has the most surface area to improve heat removal. You can use a smaller cross section that way, provided it still passes the thermal rise tests that the product needs to pass for UL or CSA approval.