Way back in the last century, (ok 12 years ago) I had to use such a beast as part of the portable appliance testing regime where I worked. Output as you say, up to 3750 volts AC, current limited to 5/10/15 mA, selected by a switch, with a deeply recessed "operate" button so it couldn't be energized accidentally. I agree they should only be used by competent persons trained in the dangers of high voltage.
With a probe carrying that kind of voltage, you could do a lot of damage to some kinds of electronic devices. But it helped pick up deteriorating insulation on double insulated tools and appliances, so yes, I believe they do have a place in the field, just a very narrowly defined one.