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A radio technician told me that DC used the same round pin plugs as AC, so correct polarity was not ensured

That was the same here. If an AC/DC radio was plugged in the wrong way round, the dial would light up, as would the tube filaments, but there would be no B+ supply so it would remain silent. Some instruction booklets added a note to reverse the plug if this happened.

As the live would be positive with respect to ground/neutral in some houses, negative in others, when fitting a 3-pin plug to a radio it was sometimes necessary to deliberately reverse the connections from the usual. And of course, when taken to a house wired on the opposite pole of the supply, it wouldn't work again until the connections were swapped over!