Yep, worked for thousands of years when Jews traveled. Not sure what changed.
You ever heard the story of the yid traveling through a harsh winter storm to finally find a an inn run by a yid. But he couldn't eat there because it wasn't under the OU
Of course, a commercial kitchen of today isn't the same as an inn of yesteryear, but even so, you'd be hard pressed to find a shliach who's "commercial" operation is not just a very busy version of his personal kitchen.
I've likely posted this before, but there was a pizza store in CH that didn't have a hechsher. I asked my father (who ran a hechsher for 40+ years and was aware of the potential issues as much as anyone) and he said, "would you eat in the owner's house?"
"Yes."
"Then you can eat his pizza."