Do I really need a newel post at every change in direction in a banister?
The handrail is primarily a safety device, so make sure you don't sacrifice that goal to save a little bit of work now.

Based on your description it doesn't sound like the spindles will really contribute much to the lateral (sideways) strength of the railing. So if you omit the intermediate posts you need to make sure the top rail is constructed with enough strength that the C shape is strong enough to support kids running into it it, elderly people supporting their weight, people leaning against it, etc.

I believe the IRC requires railings to be able to support a 200 lbs load at any point in any direction. If you think you can build the top railing with enough strength that someone can push on it with 200 lbs of force, go for it. Personally it seems like it would be a lot easier to add the extra posts.