How to compensate for leading power factor?
The capacitor in a power supply following the bridge rectifier is not causing a phase shift in the current. Instead, it is contributing to harmonic distortion of the current waveform, which is a different method of creating a poor power factor.

When you remove the capacitor, the conduction through the rectifier is more continuous. When you add the capacitor, the conduction now occurs only in short pulses at the peak of the voltage waveform.

Putting an inductor in parallel with such a load would solve nothing &mdash; you would now have a lagging current component PLUS a harmonic distortion component.

However, putting an inductor in series with such a load can have benefits. It will filter out the higher-frequency components of the harmonic distortion by forcing the rectifier diodes to switch on and off more slowly. Note that it will still cause a lag in the current relative to the voltage, but you can probably find a "sweet spot" value for the inductance that balances the two effects to create the best overall power factor.