All power supplies have a sound. "Properly designed" is not a static thing. The more you know (by listening tests) the more you know that changing one cap or diode or whatever on a power supply makes a serious difference in sound.....as I stated before, how you mount a linear power transformer makes a sonic difference. One advantage of linear power supplies is that they are simple (especially, if unregulated). So there is less listening tests to do. Switching supplies are lighter and take less space....they also run at higher frequencies so there is no 60 hz ripple to filter but they need high frequency filtering....hence, usually an inductor is series with the output.
I learned a lot about how parts effect sound in the early 80s when designing a power supply for the Sota turntable.....this was a 30 volt pre-regualtor. There was already a 12 volt regulator inside the turntable and all it was doing was spinning a belt with a motor. But every single thing I did to this 30V pre-regualor changed the sound.....even the power cord.......what was really interesting was all 4 power transformers I tried had completely different sounds. What a crazy game this is. So, what is properly designed? Is it something you do with theory or do you have to listen like crazy?.......only to find out later in time there is even a better way to get better sound......it never ends.
The best amps to mod are the ones that sound the best stock. I modded the latest IcePower IceEdge ones.....but would not recommend it or any other IcePower modules......they are not bad....just not as good as: the VTV amps using the Purifi modules or latest Hypex NCX500 modules, the VTV D300 GaN amp, the new Nilai amps, the Orchard amps, the LSA Voyager and all the Peachtree GaN amps. All these sound great stock......and much better modified. Of course, the Atmasphere amps would sound much better modded but usually if someone spends that kind of money they are afraid of mods.....plus they would not be manufacturer approved.
The two main types of mods I do are parts replacement and also parts removal (most gear has parts that are not needed that mess up the sound....for instance, all the hardware on a toroidal transformer........or extra switches, connectors, and wire, etc. not needed). I also damp things, add mass and also can add modified Wima bypass caps on the power supply....etc.