Grumpy_Mike:
But there is no physical direct contact between the primary and secondary coils.
The only separation is the tiniest fraction of an inch of two layers of insulator. I keep going back to the sentence '...a large industrial mixer that I use. It's from probably the 1960s and everything is ancient on it.' The grandkids of the people who designed and built that machine could be operating it today. The laptop that OP plugs into it today has more computing horsepower by itself than existed in the entire world at that time. With care it'll last another couple of generations. (The machine that is, CERTAINLY not the laptop! LOL!!!)
Belt and braces if you like but there is no rational about it.
One little oopsie and the machine is toast. I'd go along with three condoms but be much more comfortable with four. 
I'd bend rebar with my teeth before I'd risk that machine.