FTL isn't even necessary. Consider the majority of tanker ships travel at bicycle speeds[1]. If you're transporting sufficiently profitable nonperishable goods in extremely high quantities, and have enough automated ships, you could have a functional interstellar supply line at a fraction of light speed.
Of course, this isn't how it's usually presented in science fiction, but that's because a sci-fi story about a non-sentient fully automated mining machine wouldn't be very interesting. Gotta get humans out there.
And they said five year plans struggled with predicting demand ;)
I'd rather go with "for any delta in mining convenience between solar systems, there exists a level of FTL magic where shipping would become economically feasible"
Perhaps space slow steaming might be an option if your goal was to make a Dyson sphere exist before the star inside burns out?
Hogwash! We can do it much faster than that. With a machine in Alpha Centauri capable of flinging rocks full of rare earth metals back towards the solar system at 1/10th the speed of light, we could be up and running in <150 years.
This feels about as realistic as most of the spacetech proposals I hear.
Of course, this isn't how it's usually presented in science fiction, but that's because a sci-fi story about a non-sentient fully automated mining machine wouldn't be very interesting. Gotta get humans out there.
1. https://en.wikipedia.org/wiki/Slow_steaming