Generation of true variable resistors is necessary in some cases, but they are limited in several regards, e.g. resistance range, accuracy and linearity of control characteristic, achievable variation ratio, control speed etc. A designer will always try to use alternative like direct voltage control.
Did you notice, that two of the three applications addressed in your post can be achived by voltage control? Obviously, it's the case with DC supply control and it's also the case with the XR2206 output voltage setting, as the datasheet reveals. Audio level control is the only application, that requires a special means like a VGA mentioned by Alex, another analog multiplier technique or e.g. a LDR or linearized FET as variable resistor.