If this was an ac circuit your analysis would be correct. It is a dc circuit. Heavy current flows into the capacitor (limited only by the total circuit impedance and the available voltage) until the capacitor charges. Each cycle sees an exponentialy decreasing current bump until the final steady state current that is the load current is all that is flowing. That low reactance helps keep the ripple at the input to the regulator as low as possible. Normally the reactance of the supply transformer limits the inrush current but care must be taken not to damage the input rectfiers if the transformer has a higher than the rectifier needs kva rating to support other secondary loads.

SMP's use feedback current limiting and much lower load side capacitances due to the high operating frequencys. The input capacitors on line operated smp's are also lower value capacitors but are much higher voltage a rough equivalance is
v1 X c1 = v2 X c2 where
v1 = line voltage c1 = input storage cap v2 output voltage c2 capacitor that would be used if this was a transformer supply for the desired dc output. Terry