Can anyone explain WHY guitar amps and other dodgy consumer gadgets are NOT properly grounded?
Other than the fact that they are so cheap, they don't want to spend the extra pocket-change it takes to do it right?
Because back in the 1950s and 1960s, there was no real notion of grounded, or even polarized, outlets, and mains wiring was as good as the training of the electrician who did the work.
So Leo Fender designed his amps with a "ground" switch, which connected one or the other leg of the amp's mains transformer to chassis via a capacitor (called "death caps" in the trade). This mitigated noise but wasn't safe.
Once proper standards were introduced and safety agencies started to require proper grounding of all equipment, designs changed to meet the requirement. You won't find an amp built from the 70s on with a two-prong power cord.
Instead of spending hours repairing a guitar amp and then kludging a dangerous setup to test it,
why not simply install the proper grounded power mains cord and bring it into the 20th century?
ALL competent amp techs will suggest to their clients that their vintage amps be properly grounded, and it's a simple fix. Or they'll suggest that the amps be retired to a glass case, unused. All of mine (including a '62 Bandmaster, a '62 Deluxe, a '64 Bandmaster, and a '66 Bassman) all shipped with ungrounded mains cords, and all have been fixed.
Back when I was a regular club sound guy, bands would roll through with amps in all states of disrepair. A lot of guys would have ground lifts ("death cubes") on their amps, and I would ALWAYS just take them away. "Why did you do that?" "I don't like people dying on my stage." The worst were the guys who purposely cut off the ground pin on the mains cord.
There is a whole other sordid tale about audio gear installed in studios where the install techs would regularly cut off mains ground pins in a futile attempt to solve buzz and hum problems caused by poorly-designed gear ("pin 1 problems") ...