And then we get into the deeper waters of the sonics of the regulators themselves. Some are slow and noisy, and intermodulate with the music. Others are fast and silent. Regulators do not all sound the same, and passive CLC supplies can have a signature too, depending on the capacitors chosen. There is no one-size-fits-all solution.
The tricky bit using regulators is bandwidth.
The output of any regulator has a certain impedance. What you are looking for is a linear impedance curve across the entire audio band. The tube regulators often had a problem with this; the output impedance rises when the regulator meets its bandwidth limit. At this frequency the regulator has to be bypassed with a capacitor that keeps the output impedance as linear as possible. It won’t be perfect- usually you wind up with a step in the output impedance at the crossover point. Too much capacitance can cause the regulator to run hotter and with tubes, you can have reliability problems that might occur when the capacitance is charged during warmup.
Solid state regulators often have much wider bandwidth so don’t usually need so much bypassing, but they can have stability problems so are often bypassed with a small capacitance at the output to prevent it oscillating.
Adding additional capacitance to the output of the regulator will do little to improve sound quality and if enough capacitance is added, will increase the heat of the regulator and could threaten its reliability.
If the regulator is properly bypassed and operated well within its limits then they will tend to be neutral.
To help the regulator along, its a good idea to do as much as you can to minimize noise at the input of the regulator. For example a PI network is helpful to reduce the amplitude of the sawtooth waveform at the regulator’s input; this will reduce the work the regulator has to do, which can reduce its operating temperature.