Dryers in the US had door switches from the very beginning, was more so a convenience feature since all early dryers only had timed drying, the dryness had to be checked manually for some items since there weren’t temperature selections on some models.That was what was in my head as well - with tumble dryers, even the basic US designs, it's been a safety standard for half a century (or more) that if you open the door and close it again, you have to press start again, exactly to prevent such accidents.
There may have been a couple out there that didn’t have a door switch out there, but everything in the Whirlpool/Kenmore, Maytag and Westinghouse stable all had door switches on them.
Another reason why door switches were added was to get a good perception and reputation. If the dryer didn’t stop when the door was opened, would have turned-off the buying public plus could cause problems with heating elements burning out and failing early on if one opened the door while in operation and of course the high limit thermostat would kick in before anything else could happen.