What benefit is there in synchronizing my switching supply to the system clock
If your switching power supply frequency is close to your system clock but not exact, you could get mixing (from nonlinearities), perhaps causing interference in your signal band in analog circuitry. Usually it's the difference ("beat") frequency, not the sum, that can come to haunt you. 

Mixing is a nonlinear operation (multiplying) and the sum and difference signals derive directly from the trig identity: 



If they're synchronized, usually such problems will be minimized (perhaps a DC offset at worst).