Okay, answering my own question then. I ran a builder half the world away, and then a fresh Nau, and unfortunately no luck.
So: I play Portugal, built a Feitoria, it later got pillaged by Barbs The AI will simply not repair it. I have open borders and in fact even an alliance with that AI. Nor my builders nor a fresh Nau can repair it. So it looks like it will stay as a smoking ruin for the rest of the game.
Is the AI too dumb to repair it and benefit from the yields? Or is it too smart as it thinks it gives me more advantage? Or did the devs overlook this? Or is this, once more, a priority issue for the AI, together with not improving luxuries in M&C or not contributing to aid requests since last patch?
Can someone confirm if it is even possible to repair a Feitoria at all, if Portugal built it on your territory?