If you run, say, the telephone wires through the same holes, they'll pick up a maddening 60 Hz hummmmmmmmmmm. You're screwed because when this is discovered, the house is finished, and it gets very very expensive to rewrite it.

The closer the low voltage wires are to the high voltage ones, and the longer the distance, the more hmmmmmmm they'll pick up.

This isn't the main reason running low and high voltage through the same conduit is not code compliant though.

The reason you don't mix low/high in the same raceway is because if exposed low/high voltage conductors come in contact with each other, the low voltage cable has a much higher chance of catching fire.

I didn't think of that. It makes sense. I did think about the low voltage wire picking up enough voltage from induction to damage equipment.

The AC voltage will induce noise onto the low voltage wire. That noise can be of a higher voltage then the low voltage and damage the equipment behind it.

See also https://en.m.wikipedia.org/wiki/Electromagnetic_induction

This isn't the main reason running low and high voltage through the same conduit is not code compliant though.

The reason you don't mix low/high in the same raceway is because if exposed low/high voltage conductors come in contact with each other, the low voltage cable has a much higher chance of catching fire.

That shouldn't happen if the cable is properly shielded, no?

Electric fields are easy to shield against with a Faraday cage, but magnetic fields are a royal pain. You can use mu-metal shielding, but that's rather expensive and only reduces the magnetic field. Technically, if you wanted to entirely shield from magnetic fields, you'd need to surround the wire with a superconductor, but that requires liquid nitrogen/helium cooling that is out of the scope of most residential work.

In practice home LV wiring is rarely shielded, maybe with CAT6 as an exception. Things like speaker wire, doorbells, vacuum control wires, etc are not typically shielded.

Also the shield needs a low impedance return path to be effective.

I'm guessing it's because the AC voltage will introduce noise on the DC low voltage current.

But like everything else it depends. Is the DC feeding something like a lightbulb or a fan? Then it probably won't matter.

Does the DC feed something that has a good low pass filter or is it an expensive AC cable with good shielding? Then it might also not matter.

None of the above should be considered be professional advice and it's probably a good rule of thumb to never mix wires like that.

If the DC is feeding your telephone, it matters a log. Hmmmmmmmmmmmmm that never ends.