Nursing caps, as you are aware, come in many shapes and sizes and are often unique to different learning institutions. Initially they all had the same function; to cover the hair completely. The size of the cap became less of an issue as hair styles changed from long to short, and were adjusted to just cover hair that was pulled together or knotted.
If there were a "symbol" it could have been in support of mankind...at least initially, or perhaps for the hypocratic oath, but that is usually associated with doctors rather than healthcare workers in general. The black band, another symbol, often found on caps of "senior" people, or trainees in the last year of school, is not as traditional as it used to be.
The nursing cap was symbolic for those intentions for which it was designed. In the changing times it does not mean that the absence of a cap means that the nurse is any less of a symbol for being loyal, humble, and supportive.