The "hot chassis" electronic products were SUPPOSED to have been constructed in such a way that no part of the energized chassis was accessible in normal operation. Pots with plastic shafts, insulated knobs, plastic hardware, insulated standoffs, etc. were all commonly used for this. Millions of 5-tube "AC/DC" radios and "hot chassis" TV sets were produced (and still are). No safety problem from the end-user perspective, but special precautions (isolation transformer) are required when troubleshooting and repairing them.
If you were getting a shock from such a unit, then something was seriously wrong. An incorrectly installed chassis mounting screw, missing insulator, or improper modifications to the unit could all cause this problem. None of the exposed metal parts (screws, handles, connectors, etc.) should be connected to the chassis ground.
Before the polarized plug was introduced, the instructions for a radio or TV often advised trying the plug in the outlet both ways, to minimise hum. Presumably, the hum would be less when the chassis was connected to the neutral side of the line.