Why is it preferable to say that the doppler effect causes a shift in frequency rather than a shift in wavelength? I often read on websites that they define the doppler effect as a change in frequency.
The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer.
In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in frequency. So it's a matter of relativity. To the traveling observer (in the source), only the wavelength is changing, to the stationary observer (experiencing the doppler shift) both frequency and wavelength have changed.