Why does the high frequency component of an image contain more noise?
There are different types of noise sources in imaging process. 

Photoelectronic

photon noise: Poisson distribution, whole spectra;

thermal noise: Gaussian distribution, white noise, whole spectra;

Impulse

salt and pepper noise: mainly high frequency noise; (@user7358 made a very good point on the reason).

line drop: part or all of a line in the image lost, can be viewed as a deterministic high frequency noise;

Structured

periodic: low frequency noise;

aperiodic: JPEG noise, low frequency too;

detector striping: calibration differences among individual scanning detectors, mainly low frequency;

If you only observe the evident noise when you zoom in the high frequency band with wavelet, I assume it is mainly the shot noise (salt and pepper). When you are doing some simulations with noise added, try (1) salt and pepper,  (2) Gaussian, and (3) Gaussian with a high-pass band applied, and observe the difference after wavelet decomposition.