All of the roads we're talking about, for the most part, are 4-lane freeways, designed to keep traffic moving at normal highway speed, even through the mountains. There are no places where we are talking about things like switchbacks or extremely steep grades.
In other words, there should be no issues at all with a compact car dealing with such curves, and I certainly wouldn't recommend driving 100 miles out of your way to avoid them (especially when you'd really just be exchanging one mountain highway for another.)
Unless you were doing something like towing, this shouldn't be an issue at all. A compact car like a Civic should be able to travel all of these roads with ease. The only way it would be a problem at all is if your car is severely overloaded, as discussed above.