Importance of series resistor at output of Rectifier
In an actual circuit, the effect of R1 is always present, whether or not there is a separate R1 installed.

If you simulate the top circuit with a zero impedance voltage source, diodes with no residual resistance, and a capacitor with zero ESR, then the current that flows during the charging pulses will be infinite, which is of course non-physical. When simulating, you should add an estimate of the transformer winding resistance as R1, as well as using diode models which include residual resistance, to get sensible charging current magnitudes. We can usually ignore capacitor ESR compared to those other two resistances.

Given the transformer resistance, wiring resistance, and the robustness of typical rectifier diodes to pulse loading, it's unlikely that you would ever need to add an explicit R1 to such a rectifier circuit to reduce the size of the charging current pulses. But I'd never say never.