Duty Cycle

why is the duty cycle usually changed by varying the on time rather than the chopping frequency

There are constant on-time PWM systems (including switch mode controllers).

Variable frequency systems have a linear relationship between time-on per cycle and the effective duty cycle of the signal. By varying the frequency, the relationship is non-linear. This can be good or bad in terms of circuit/firmware complexity and loop stability.

The output of a PWM switch also is often passed to a low pass filter (e.g. the inductor and output cap in a buck converter). Operating at a constant frequency simplifies the determination of the values for these components and typically offers lower ripple on the output for a given set of LC values (because the dv/dt of the charge portion of the cycle is variable instead of constant).

I suspect one of the reasons constant on-time is used for switch mode controllers is that you just keep extending the time between pulses at very low loads instead of having the logic associated with pulse skipping common in constant frequency converters.

There are certain modulation technique, namely PWM, PFM and PSM.

PWM is the most basic one by varying on time rather than chopping frequency.

One of the reason for its popularity is related to its comprehensive theoretical framework in control theory and design.