And you don't need rudder input or any aileron input because of crosswind, and other bits that falls into "technically correct but not particularly relevant" territory.

It's fun to see/feel planes do stuff "on their own" (eg making them oscillate, or level on their own, or feeling ground effect, or even your own wake on steep turns) but it's not something you'd want to rely on (maybe with the exception of ground effect on short field takeoffs, but I digress).