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.